mode i fracture toughness and tensile strength

MODE I FRACTURE TOUGHNESS AND TENSILE STRENGTH

INVESTIGATION ON MOLDED SHOTCRETE BRAZILIAN SPECIMEN

A THESIS SUBMITTED TO

THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES

OF

MIDDLE EAST TECHNICAL UNIVERSITY

BY

TUĞÇE TAYFUNER

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR

THE DEGREE OF MASTER OF SCIENCE

IN

MINING ENGINEERING

SEPTEMBER 2019

Approval of the thesis:



submitted by TUĞÇE TAYFUNER in partial fulfillment of the requirements for the

degree of Master of Science in Mining Engineering Department, Middle East

Technical University by,

Prof. Dr. Halil Kalıpçılar

Dean, Graduate School of Natural and Applied Sciences

Prof. Dr. Celal Karpuz

Head of Department, Mining Engineering

Prof. Dr. Levend Tutluoğlu

Supervisor, Mining Engineering, METU

Examining Committee Members:

Prof. Dr. Celal Karpuz

Mining Engineering, METU

Prof. Dr. Levend Tutluoğlu

Mining Engineering, METU

Assoc. Prof. Dr. Mehmet Ali Hindistan

Mining Engineering, Hacettepe Uni.

Date: 13.09.2019

iv

I hereby declare that all information in this document has been obtained and

presented in accordance with academic rules and ethical conduct. I also declare

that, as required by these rules and conduct, I have fully cited and referenced all

material and results that are not original to this work.

Name, Surname:

Signature:

Tuğçe Tayfuner

v

ABSTRACT



Tayfuner, Tuğçe

Master of Science, Mining Engineering

Supervisor: Prof. Dr. Levend Tutluoğlu

September 2019, 141 pages

Tensile opening mode I loading state is important for shotcrete-concrete type

materials, since these are weak under tension. Brazilian type splitting tests are

commonly used for checking the structural effectiveness of concrete in opening mode.

Tensile strength is measured indirectly by these tests.

In concrete industry, beam tests under three- and four-point bending loads are used to

measure tensile strength and mode I fracture toughness of beams and columns under

almost pure tensile loading state. However, some structural parts are under

compression and indirect tensile loading may result in these. Flattened Brazilian Disc

(FBD) is a modified splitting type geometry. It is preferred due to its simplicity of

specimen preparation and the compressive load application. Testing this geometry

under compression provides means to measure both tensile strength and mode I

fracture toughness with a single specimen and test.

This work is original in the sense that FBD geometry and the testing method are

successfully applied to measure the tensile strength and fracture toughness of molded

shotcrete with a water/cement ratio of 0.5. Molds are designed in different sizes and

3D printing technology are used to produce these accurately in desired geometries.

vi

The aim of this study is to investigate the relations between fracture toughness,

specimen size, curing time and the tensile strength of shotcrete for a particular mixture

design. Loading angle that is defined as the angle between the paths drawn from the

specimen center to the edges of flattened loading ends, are kept constant at 22° in all

testing work. This corresponds to a half of the flattened end/radius ratio of L/R=0.19.

For investigating the effect of specimen size on the fracture toughness, specimen

diameters were varied between 100 mm and 200 mm. Curing time was constant as 7-

day for this group of tests. Fracture toughness of shotcrete was found to increase from

0.93 to 1.46 MPa√m while specimen diameters were changing between 100 mm to

200 mm.

The effect of curing time on fracture toughness was investigated with constant 160

mm diameter disc specimen geometry. One to seven-day air cured FBD specimens

were tested. It was found that mode I fracture toughness of shotcrete increased from

0.66 to 1.18 MPa√m with increasing curing time.

The tensile strength calculated from Flattened Brazilian Disc tests were compared to

the results of the conventional Brazilian Disc tests. Processing the experimental

results, a size independent fracture toughness/tensile strength ratio was proposed for

concrete type of materials.

Keywords: Shotcrete, mode I fracture toughness, Flattened Brazilian disc method, size

effect, curing time

vii

ÖZ

BRAZİLYAN DÖKÜLMÜŞ PÜSKÜRTME BETON NUMUNELERİNDE

MOD I KIRILMA TOKLUĞUNUN VE ÇEKME DAYANIMININ

İNCELENMESİ

Tayfuner, Tuğçe

Yüksek Lisans, Maden Mühendisliği

Tez Danışmanı: Prof. Dr. Levend Tutluoğlu

Eylül 2019, 141 sayfa

Beton-püskürtme beton tipi malzemelerin gerilme yüklenmesi karşısında zayıf

olduklarından mod I diye isimlendirilen açılma modu, bu tarzda numunelerin kırılma

tokluklarının incelenmesi için en kritik yükleme modudur. Düzleştirilmiş Brazilyan

disk yöntemi bu yükleme modunda kırılma tokluğu araştırılması yapılması için şekil

yapısından ötürü önerilen bir yöntemdir.Bu test yöntemi kullanılarak çekme

dayanımının dolaylı yolla elde edilmiştir.

Beton endüstrisinde, üç ve dört noktalı eğilme yükleri altındaki kiriş testleri, mod I,

neredeyse saf çekme yükü durumunda kirişlerin ve kolonların çekme dayanımını ve

kırılma tokluğunu ölçmek için kullanılır. Bununla birlikte, yapısal olarak bazı bölgeler

sıkıştırma etkisi altında kalabilir ve bu bölgeler dolaylı çekme yükü ile sonuçlanabilir.

Düzleştirilmiş Brezilyan Disk (FBD), değiştirilmiş bir ayrılma tipi geometridir. Bu

geometri hem sıkıştırma altında test edildiği hem de numune hazırlamasında sağladığı

kolaylıktan dolayı tercih edilmektedir. Sıkıştırma yükü altında test edilen bu

numuneden hem Mod I kırılma tokluğunu hem de çekme mukavemeti ölçülebilir.

Bu çalışma, FBD geometrisi ve test yönteminin, 0.5 su çimento oranına sahip

kalıplanmış püskürtme betonun çekme dayanımını ve kırılma tokluğunu ölçmek için

başarılı bir şekilde uygulanması anlamında orijinaldir. Kalıplar farklı boyutlarda

viii

tasarlanır ve bunları istenen geometrilerde doğru şekilde üretmek için 3D baskı

teknolojisi kullanılır.

Bu çalışmanın amacı, seçilen beton karışım tasarımı için, püskürtme betonun kırılma

tokluğunun numune büyüklüğü, kür süresi ve çekme dayanımı ile ilişkisini

incelemektir.

Numunenin merkezinden düzleştirilmiş yükleme uçlarının kenarlarına doğru çizgiler

olduğu farzedilirse bu çizgiler arasındaki açı olarak tanımlanan yükleme açısı, tüm

test çalışmalarında 22 ° olacak şekilde sabit tutulur. Bu açı düzleştirilmiş yükleme

yüzeyinin uzunluğunun yarısının yarıçapa oranı olan, L/R = 0.19 ‘a karşılık

gelmektedir.

Numune büyüklüğünün mod I kırılma tokluğuna etkisi araştırılırken, sabit karışım

oranı, sabit yükleme açısı ve 7 gün olarak belirlenen sabit kür süresinde çaplar 100

mm ile 200 mm arasında değiştirilmiştir. Sonuçlar mod I kırılma tokluğunun, numune

çapları 100 mm ile 200 mm arasında değişirken, 0.93-1.46 MPa√𝑚 aralığında

değiştiğini göstermektedir.

Devamında yapılan kür süresinin kırılma tokluğu üzerindeki etkisinin araştırıldığı

çalışmada çapı 160 mm olan numuneler ile çalışılmış, kür süresi 1 gün ile 7 gün arası

değişirken karışım oranı, yükleme açısı ve numune çapı sabit tutulmuştur. Bu çalışma

sonucunda ise 1 gün ile 7 gün arasında değişen kür alma sürelerinde püskürtme

betonun mod I kırılma tokluğu 0.66-1.18 MPa√𝑚 arasında değişmiştir.

Tüm bunlara ek olarak, çalışmanın son bölümünde Düzleştirilmiş Brazilyan disk

testlerinen çekme dayanımı hesaplanması ve bunların geleneksel Brazilyan disk test

sonuçları ile karşılaştırılması çalışılmışır. Elde edilen deney sonuçlarından ve bu

sonuçların excel grafiklerinden, beton tipi Düzleştirilmiş Brazilyan Disk

numunelerinde,160 mm çapa sahip olanlar için, numune çapından bağımsız kırılma

tokluğu/ çekme dayanımı oranı (katsayısı) geliştirilmiştir.

ix

Anahtar Kelimeler: Püskürtme beton, mod I kırılma tokluğu, düzleştirilmiş Brazilyan

disk yöntemi, boyut etkisi, kür süresi

x

To My Family

xi

ACKNOWLEDGEMENTS

I would like to express my deepest gratitude to my supervisor Prof. Dr. Levend

Tutluoğlu for his patient guidance, scientific insight, precious comments and trust in

me. I want to thank to the examining committee the members, Prof. Dr. Celal Karpuz

and Assoc. Prof. Dr. Mehmet Ali Hindistan for their valuable contributions.

I am deeply grateful to Selin Yoncacı, who will soon get her PhD degree, for not

leaving me alone during the whole process and for answering all my questions all that

time. Moreover, I want to thank my chief engineer Koray Önal and my manager Ömer

Şansal Gülcüoğlu for their support during my thesis period.

I would like to thank my friends, research assistants Enver Yılmaz and Ceren Karataş

Batan for staying with me in the laboratory when it necessary and no matter how long

it took.

I would like to show my gratitude to my dearest friends Gizem Özcan, Müge Öztürk, Onur

Can Kaplan. They are always with me, in my best and worst times. I also want to thank

Hazal Varol, Buse Ceren Otaç, Merve Özköse and Elif Naz Şar for their support and

motivation.

I would also like to extend my thanks to Hakan Uysal for his support during my

laboratory works.

I would like to offer all my loving thanks to my family Senar Tayfuner, Serdal

Tayfuner and Berk Tayfuner for their limitless support and encouragement.

Finally, I want to express my deepest gratitude and appreciation to Onur Can Yağmur

being with me whenever I need. I will never forget your support and help during this

process.

xii

TABLE OF CONTENTS

ABSTRACT ................................................................................................................ v

ÖZ ............................................................................................................................ vii

ACKNOWLEDGEMENTS ........................................................................................ xi

TABLE OF CONTENTS .......................................................................................... xii

LIST OF TABLES ..................................................................................................... xv

LIST OF FIGURES ................................................................................................. xvii

LIST OF ABBREVIATIONS .................................................................................. xxii

LIST OF SYMBOLS .............................................................................................. xxiii

CHAPTERS

1. INTRODUCTION ................................................................................................ 1

1.1. General .............................................................................................................. 1

1.2. Statement of the Problem .................................................................................. 2

1.3. Objectives of the Study ..................................................................................... 3

1.4. Methodology of the Study ................................................................................. 4

1.5. Organization of Thesis ...................................................................................... 6

2. THEORETICAL BACKGROUND OF FRACTURE MECHANICS ................ 7

2.1. History of Fracture Mechanics .......................................................................... 7

2.2. Basics of Fracture Mechanics ........................................................................... 9

2.2.1. Fracture Modes ........................................................................................... 9

2.2.2. Stress Intensity Factor .............................................................................. 10

2.2.3. Fracture Toughness .................................................................................. 10

2.2.4. Linear Elastic Fracture Mechanics ........................................................... 12

xiii

2.3. Fracture Toughness Testing with Flattened Brazilian Disc Test Method ....... 13

2.4. Fracture Mechanics of Concrete ...................................................................... 18

3. SHOTCRETE MIXTURE SETUP ..................................................................... 21

3.1. Shotcrete Mixture Ingredients ......................................................................... 21

3.1.1. Portland Cement ....................................................................................... 22

3.1.2. Aggregate .................................................................................................. 23

3.1.3. Water ......................................................................................................... 26

3.1.4. Admixtures/Additives ............................................................................... 26

3.2. 3D Molds and Recipe for Shotcrete ................................................................ 27

3.3. Preparation of Shotcrete Samples .................................................................... 29

4. TESTING FOR MECHANICAL PROPERTIES OF SHOTCRETE ................ 33

4.1. Static Deformability Test ................................................................................ 34

4.2. Indirect Tensile Strength Test (Brazilian Disc Test) ....................................... 41

4.3. Tensile Strength Estimation from Brazilian Disc Tests .................................. 44

4.3.1. Wang’s Approach ..................................................................................... 45

4.3.2. Keles and Tutluoglu’s Approach .............................................................. 50

5. MODE I FRACTURE TOUGHNESS TESTS .................................................. 55

5.1. Fracture Toughness Testing Work .................................................................. 55

5.2. Computation for Fracture Toughness .............................................................. 58

5.3. Investigation of Size Effect on Mode I Fracture Toughness of Shotcrete ...... 61

5.3.1. Tables for Individual Fracture Toughness Test Results ........................... 64

5.4. Investigation of Curing Time on Mode I Fracture Toughness of

Shotcrete/Concrete Type of Specimen ................................................................... 66

5.4.1. Tables of Results for Curing Time Investigation...................................... 67

xiv

6. EXPERIMENTAL RESULTS AND DISCUSSION ......................................... 69

6.1. Tables of Results for Size Effect Investigation ............................................... 70

6.2. Effect of Curing Time on the Fracture Toughness ......................................... 75

6.3. Tensile Strength - Fracture Toughness Investigation ..................................... 78

7. CONCLUSION AND RECOMMENDATIONS ............................................... 83

REFERENCES .......................................................................................................... 87

APPENDICES

A. Static Deformability and Brazilian Disc Test Graphs ....................................... 95

B. Mode I Fracture Toughness Test Graphs ......................................................... 103

C. Crack Length Measurement of Mode I Fracture Toughness Test Samples ..... 127

xv

LIST OF TABLES

TABLES

Table 3.1. Pycnometer test parameters ...................................................................... 25

Table 3.2. Dimensions of the specimens extracted from the molds ........................... 28

Table 3.3. Recipe for all diameters ............................................................................ 29

Table 4.1. Static deformability test results ................................................................. 36

Table 4.2. Brazilian disc test results .......................................................................... 42

Table 4.3. Average tensile strength from Wang’s correction coefficient .................. 48

Table 4.4. Tensile strength calculation from Keles and Tutluoglu’s correction

coefficient ................................................................................................................... 52

Table 5.1. Dimensions of shotcrete specimens .......................................................... 63

Table 5.2. t, 2ace, ace/R, Pmin, and KIC values of FBD specimens having 100 mm

diameter ...................................................................................................................... 64


diameter ...................................................................................................................... 64


diameter ...................................................................................................................... 64


diameter ...................................................................................................................... 65


diameter ...................................................................................................................... 65


diameter ...................................................................................................................... 65

Table 5.8. t, Pmin, and KIC values of FBD specimens having 160 mm diameter with 1

day cured .................................................................................................................... 67


days cured .................................................................................................................. 67

xvi


days cured .................................................................................................................. 67


days cured .................................................................................................................. 68


days cured .................................................................................................................. 68

Table 6.1. All test results for investigation of size effect on the fracture toughness . 71

Table 6.2. Average fracture toughness results of FBD specimens with corresponding

diameters .................................................................................................................... 72

Table 6.3. All test results for investigation of curing time on the fracture toughness

................................................................................................................................... 76

Table 6.4. Average FBD test results according to the changing curing time ............ 76

Table 6.5. Tensile strength calculation from Wang’s correction coefficient ............ 79

xvii

LIST OF FIGURES

FIGURES

Figure 2.1. Leonardo da Vinci fracture test setup (Gross, 2014) ................................. 7

Figure 2.2. Galileo Galilei tensile test setup (Gross, 2014) ......................................... 8

Figure 2.3. Fracture modes (Key to Metals Database, 2010)....................................... 9

Figure 2.4. The Brazilian Disc specimen under the uniform arc loading (at left) and

the Flattened Brazilian Disc specimen under the uniform diametral compression (at

right) (Wang & Wu, 2004) ......................................................................................... 15

Figure 2.5. The geometric representation of Flattened Brazilian Disc (Keles and

Tutluoglu, 2011) ......................................................................................................... 16

Figure 2.6. A typical load displacement curve (Wang and Xing, 1999) .................... 17

Figure 2.7. Maximum dimensionless stress intensity factor represented by Wang and

Xing (Wang and Xing, 1999) ..................................................................................... 18

Figure 3.1. Cement ..................................................................................................... 22

Figure 3.2. Aggregate ................................................................................................. 24

Figure 3.3. Pycnometer tests ...................................................................................... 25

Figure 3.4. Additives .................................................................................................. 26

Figure 3.5. Drawing of FBD mold in SolidWorks ..................................................... 27

Figure 3.6. Used molds with varying diameters 100 mm to 200 mm ........................ 28

Figure 3.7. UTEST mixer........................................................................................... 30

Figure 3.8. Lubrication process .................................................................................. 31

Figure 3.9. Casted Shotcrete ...................................................................................... 31

Figure 3.10. Successful and unsuccessful casting products ....................................... 32

Figure 4.1. Prepared molds for conventional testing ................................................. 33

Figure 4.2. Cylindrical samples taken out of molds for static deformability test ...... 34

Figure 4.3. Static Deformability Test Setup............................................................... 35

Figure 4.4. Lateral strain vs axial strain graph ........................................................... 37

xviii

Figure 4.5. Stress vs lateral strain and axial strain graph .......................................... 37

Figure 4.6. Development of Young’s modulus with early age of shotcrete compiled

from various research by (Chang, 1994) ................................................................... 38

Figure 4.7. UCS results of various researchers compiled by Chang (1994) .............. 39

Figure 4.8. Variation of Poisson’s ratio with time (Aydan et al., 1992) ................... 40

Figure 4.9. Brazilian Disc Test set up ........................................................................ 42

Figure 4.10. A typical Brazilian Disc sample with central crack clearly visible ....... 43

Figure 4.11. Force-Displacement curve of a Brazilian Disc test specimen ............... 44

Figure 4.12. Specimen subjected to a uniform diametric loading (Wang et al.,2004)

................................................................................................................................... 47

Figure 4.13. Tensile strength versus specimen diameter using Wang approach ....... 49

Figure 4.14. The ratio of the tensile strengths from FBD and BD with varying diameter

................................................................................................................................... 50

Figure 4.15. Tensile strength versus specimen diameter using Keles and Tutluoglu

approach ..................................................................................................................... 52

Figure 4.16. The ratio of tensile strengths from FBD and BD with related diameters

................................................................................................................................... 53

Figure 4.17. Bazant’s size effect investigation (Bazant et al., 1991) ........................ 54

Figure 5.1. A typical Force-Displacement curve of a Flattened Brazilian Disc test . 57

Figure 5.2. A typical experimental critical crack length measurement ..................... 58

Figure 5.3. Name code of tested FBD specimens ...................................................... 62

Figure 5.4. FBD specimen geometry ......................................................................... 63

Figure 5.5. Name code of tested FBD specimens ...................................................... 66

Figure 6.1. KIC values of FBD tested specimens having various diameters .............. 73

Figure 6.2. Dimensionless critical crack length of FBD tested specimens ............... 74

Figure 6.3. Average KIC values changing with the curing time of shotcrete ............. 78

Figure 6.4. The relation between σt W and KIC ........................................................... 79

Figure 6.5. The relation between σt,K T and KIC ......................................................... 80

Figure 6.6. Dimensionless toughness over tensile strength ratio ............................... 81

Figure 0.1. Static deformability test graph of S_SD_1 .............................................. 95

xix









Figure 0.10. Static deformability test graph of S_SD_5 ............................................ 99

Figure 0.11. Brazilian Disc test graph of S_BD_1 .................................................. 100





Figure 0.16. Flattened Brazilian Disc test graph of S100_s1 ................................... 103
















xx

Figure 0.32. Flattened Brazilian Disc test graph of S160_s1 .................................. 111














Figure 0.46. Flattened Brazilian Disc test graph of S160-1D-s1 ............................. 118















Figure 0.61. FBD test crack measurement of the sample S100_s1 ......................... 127

xxi

Figure 0.62. FBD test crack measurement of the sample S100_s2 .......................... 127





























xxii

LIST OF ABBREVIATIONS

ABBREVIATIONS

2D: two-dimensional

3D: three-dimensional

BDT : Brazilian disc test

CB : Chevron bend

CCNBD : Cracked chevron notched Brazilian disc

CPD: Crack propagation direction

CPE8: Continuum plane strain eight noded element

CSTBD : Cracked straight through Brazilian disc

FBD : Flattened Brazilian disc

ISRM : International Society for Rock Mechanics

LEFM: Linear elastic fracture mechanics

LVDT: Linear variable differential transformer

MTS: Maximum tangential stress

SCB : Semi-circular bending

SIF: Stress intensity factor

SNDB : Straight-notched disc bending

SR: Short-rod

UCS : Uniaxial Compressive Strength

xxiii

LIST OF SYMBOLS

SYMBOLS

a: half of crack length

A: mesh size

A: andesite

D: specimen diameter

de: distance of crack tip to central load application point

E: Elastic Modulus

G : energy release rate

Gc : critical energy release rate

J: J integral

K: stress intensity factor

KC: critical stress intensity factor

𝐾I : mode I stress intensity factor (opening mode)

𝐾II : mode II stress intensity factor (shearing mode)

𝐾III : mode III stress intensity factor (tearing mode)

KIc : mode I fracture toughness

KIIc : mode II fracture toughness

L: half of flattened length

P: applied concentrated load

Pmax: failure load

xxiv

Pmin: local minimum load

R: disc radius

rc: radius of contour integral region

S11 : normal stress in x-direction

S22 : normal stress in y-direction

S33 : normal stress in z-direction

S12 : shear stress in xy-direction

S: span length

t: specimen thickness

Y : dimensionless stress intensity factor

YI : mode I dimensionless stress intensity factor

YII : mode II dimensionless stress intensity factor

Yımax : maximum dimensionless stress intensity factor

w : projected width over loaded section

: half of loading angle

ε : Strain

σ : stress

𝜎1 : maximum principal stress

𝜎3 : minimum principal stress

𝜎𝑡 : tensile strength

α : a/R

xxv

τ : shear stress

µ: shear modulus

𝜗 : Poisson’s Ratio

θ : crack propagation angle

tc: curing time in days

𝜎𝑡: tensile strength

1

CHAPTER 1

1. INTRODUCTION

1.1. General

According to the data from the National Institute for Science and Technology and the

Bettelle Memorial Institute, in one year 119 billion dollars were spent because of

fracture related failures in 1983. The money has an incontrovertible significance;

however, the price of many failures in human life and also physical injuries are more

important than the dollars, (Anderson, 2005).

Defects in the materials, lack of information about the loading or environment,

improper design and defects in structures can cause catastrophic failures.

In the respect of both structural and mining engineering, Rossmanith said that the main

questions are respectively: “how the failure load of these flawed structures can be

estimated? Which kind of combinations of load and parameters of flaw geometry

causes the failure? Moreover, which material variables are the fracture process

conducted by?” (Rossmanith, 1983).

In 1950’s and 1960’s, Fracture Engineering eventually arise to find out the causes of

cracks in various engineering materials. There are several engineering materials such

as metal, rock, concrete and ceramics. Rock fracture mechanics is the science that

identifies how the crack starts and disseminates under the applied loads in rock

engineering. The crack resistance at the beginning of the crack growth is specified by

fracture toughness parameter and this is a very active area of the current research.

The stability of underground engineering structures may be possible by supporting the

cavities opened in the structures rapidly with lower cost. Shotcrete technology has

improved recently with the findings and innovations in installation equipment and

2

material technology. Although, shotcrete applications go back a long way around the

beginning of 20th century, structural integrity of shotcrete is a relatively a new field

of research area which needs to be investigated in detail. Nowadays, underground

mine openings, tunnels, and the galleries of many purposes are being stabilized by

shotcrete support systems. As most of the time shotcrete is applied just after its

preparation on site, it is difficult to conduct a detailed laboratory analysis. Detailed

laboratory testing can be done if a proper mixture of shotcrete can be prepared; so that

shotcrete in the field practice is simulated closely.

1.2. Statement of the Problem

Although, shotcrete is a widely used heterogeneous material that particularly used as

a support system, the crack behavior of it has not been focused enough even though

one of the most important weakness of it is cracks. Most of the studies on shotcrete is

based on laboratory tests to determine its mechanical properties, strength, setting time

or rebound rate. So far, not enough attention is paid to the fracture mechanics and

crack propagation characteristics of shotcrete, which is one of the most important

consideration for the field of engineering.

Mode I fracture toughness is a measure of the fracture energy to propagate a crack

under tension in materials. This parameter is important also in the preventing efforts

of propagation of a pre-existing defect. Fracture toughness tests are commonly carried

out with beam and disc or cylinder-type specimen geometries. One current trend in

fracture toughness testing is to minimize the specimen geometry effect on pure tensile

mode crack opening. Specimen geometry is associated with a size effect issue.

Size effect on facture toughness of rocks has been frequently investigated. However,

rock fracture toughness testing is usually restricted to the core sample diameters which

may go up to around 100 mm in practice. It has not been possible to work with large

range of diameters. Sizes of specimens were limited, in particular in circular

geometries such as FBD geometry, depending on the diameter of the core drilling

3

machine. Research on internal characteristics and mechanical properties of shotcrete

is still in progress in literature. It is worth to carry out an investigation about the size

effect on fracture toughness of cementitious material.

A few studies investigate the shotcrete behavior at early ages of curing. There is a

need for information on crack formation or crack mechanisms, since shotcrete is used

to provide temporary surface control for local stability before the primary support is

installed. Because the shotcrete must become self-supporting before miners and

equipment can work safely underneath, the curing characteristics of the shotcrete are

critical to the speed of the mining cycle. Thus, in order to understand the time-

dependent response of fracture behavior in shotcrete, more research is to be done on

the basis of laboratory tests.

Under mode I fracture loading, the opening mode, brittle or quasi-brittle materials

commonly yield in tension. Thus, one might expect that there is a relationship between

the fracture toughness and the tensile strength of shotcrete.

Therefore, studying the initiation of cracks or fracture toughness of the shotcrete

specimens depending on the geometry and the curing time is a challenging topic. The

relation of the fracture toughness to the tensile strength of the shotcrete is an

innovative area that needs to be investigated.

1.3. Objectives of the Study

The main objectives of performing this thesis are to understand the relation between

fracture toughness of shotcrete with the specimen size, curing time and the tensile

strength for a particular mix design.

4

1.4. Methodology of the Study

Cementitious materials like shotcrete-concrete generally exhibit high compressive

strength, low tensile strength. So the mode I, in other words tensile opening mode is a

crucial loading mode for not only shotcrete but also for brittle materials such as rocks.

ISRM and ASTM suggested many methods to measure the rock fracture toughness.

The main proposed methods by International Society for Rock Mechanics (ISRM),

are:

Short rod (SR) (Ouchterlony, 1988),

Chevron bend (CB) (Ouchterlony, 1988),

Cracked chevron notched Brazilian disc (CCNBD) (Fowell, 1995)

Semi-circular bending (Kuruppu et al., 2015)

Brazilian type methods which were preferable since relatively simple both in specimen

preparation and also compressive loading on disc specimens while testing include;

Cracked chevron notched Brazilian disc (CCNBD), (Sheity, D. K.,

Rosenfield, A. R., & Duckworth, W. H. (1985)

Cracked straight through Brazilian disc (CSTBD)

Semi-circular bending test (SCB) (Chong and Kuruppu, 1984)

Brazilian disc (BD) (Guo et al., 1993)

Flattened Brazilian disc (FBD) (Wang and Xing, 1999)

The reason for selection of the Flattened Brazilian Disc method is the easiness of

sample preparation and testing procedure. Compressive loading in fracture testing and

indirectly generating tensile splitting are attractive for brittle materials. Although, it is

necessary to prepare a very precise samples for FBD testing, the usage of 3D printing

technology for shotcrete casting process provided the desired geometric accuracy.

Moreover, 3D printing technology made preparation of specimens in different sizes

5

possible. A wide range of specimen with varying diameters were tested to measure

tensile strength and mode I fracture toughness of shotcrete.

The experimental work started with the preparation of the shotcrete specimens. In the

preparation of shotcrete samples, attention was paid to use the same ingredients for

each sample and to prepare with the same equipment under the same laboratory

conditions in order to interpret the test results correctly. Five samples were molded

and tested for each group of varying specimen sizes in order to increase statistical

quality of the test results.

For all tests, MTS 815 Rock Testing Machine in laboratory was used. Five specimens

were prepared for each diameter and curing time group.

First, conventional mechanical property testing work was conducted. Static

deformability test and uniaxial compressive strength tests were conducted in order

both to check the mechanical properties of the shotcrete and to validate the mixture

according to its mechanical properties in the literature. The conventional Brazilian

disc test was conducted next to measure the tensile strength with regular testing

method.

Finally, as the main part, mode I fracture toughness tests with Flattened Brazilian Disc

geometry were carried out to split the samples into two. One investigation was the size

effect on fracture toughness with constant curing time and changing diameters and the

second one was performed to analyse the effect of curing time on fracture toughness

with constant diameter and various curing time. Moreover, in order to determine the

relation between fracture toughness and the tensile strength, conventional Brazilian

test results were compared to the results of Flattened Brazilian Disk tests. For the

evaluation of experimental results, equations from a similar work were adopted.

6

1.5. Organization of Thesis

This thesis is divided into six chapter. Following this introduction. Chapter 2 presents

a general review of the literature about the basics of fracture mechanic and its

significance for the main research problem. In Chapter 2, description of the different

fracture toughness testing methods is provided. Experimental method used to

determine mode I fracture toughness and its background are explained as well as

fracture mechanics of shotcrete. Chapter 3 presents a description of the properties of

shotcrete mixture and its ingredients. It continues with the shotcrete mix design and

laboratory work related to the casting process. Chapter 4 presents a detailed

description of the laboratory work and the results of all conventional experimental

study, including static deformability tests, Brazilian disc test, and the most importantly

Flattened Brazilian Disc tests to investigate fracture toughness and to the factors

affecting its value. Chapter 5 presents evaluation of the results, discussion of the all

experiments carried out, and the interpretation of these results with the help of

previous studies in literature. Finally, Chapter 6 presents conclusion and the findings

of this study as well as recommendations for further research in this field.

7

CHAPTER 2

2. THEORETICAL BACKGROUND OF FRACTURE MECHANICS

2.1. History of Fracture Mechanics

In the early Renaissance, the concept of fracture had been scientifically evaluated as

scaling of fracture and experiments were conducted on iron wires by Leonardo da

Vinci for the first time (1452-1519), (Figure 2.1), (Gross,2014).

Figure 2.1. Leonardo da Vinci fracture test setup (Gross, 2014)

Afterwards, Galileo Galilei (1564–1642) who was known as the founder of modern

mechanics by his contributions from his well-known “Dialog”, made correct

inferences that the fracture forces of column under tension were related to the cross

sectional area, and also he stated that the bending moment was the crucial loading type

for the fracture of beams, (Figure 2.2), (Cotterel, 2002).

8

Figure 2.2. Galileo Galilei tensile test setup (Gross, 2014)

The most punctual work was done by Griffith (1921). He carried out an analysis for

actual cracks. Even though, Griffith’s theory was so important, it was limited for some

highly brittle materials such as glass. In the early 1960s, with the development of the

discipline that we called “fracture mechanics”, Irwin (1958) who was a professor from

Lehigh University, examined plasticity in detail. He extended the Griffth’s theory.

Irwin proposed that the stress intensity factor concept could be used for the calculation

of stress field around the crack tip.

Applications of engineering fracture mechanics to brittle materials developed with an

important delay in comparison to ductile materials. Considering the underground

mines, tunnels in galleries etc., rock fracture problem has a significant role in

collapses. At the early sixties, Griffith’s model found the roles in applications

involving stone and concrete type materials. The friction between crack faces was

established byMc Clintock and Walsh (1962). They modified Griffith’s theory and

investigated the crack closure in compression, whereas Kaplan (1961) have published

the first experimental study about the possibility of applying linear elastic fracture

mechanics to concrete. In 1965 Bieniawski and Hoek was performed the early research

about rocks, in South Africa, where mine disappointments were earnest issues to be

comprehended (Ceriolo and Tommaso, 1998).

9

2.2. Basics of Fracture Mechanics

2.2.1. Fracture Modes

There are three main ways named as mode I, mode II and mode III for cracks to initiate

and propagate in a material, (Figure 2.3).

Figure 2.3. Fracture modes (Key to Metals Database, 2010)

Mode I: In mode I, also known as tensile opening mode, direction normal to the crack

plane separates the faces of the cracks.

Mode II: In mode II, also named as in-plane sliding or shear mode, both crack faces

are in the direction of crack front normal.

Mode III: In mode III, also named as the tearing or out of plane mode, the crack faces

are sheared parallel to the crack front.

Crack formations can occur by any of these three modes. Moreover, combinations of

these modes are also possible such as mode I and mode II can occur simultaneously.

In such a case it is called as mixed mode. Mode I is the essential failure mode for

brittle material since brittle materials are weak under tension.

10

2.2.2. Stress Intensity Factor

Stress intensity factor, K is used for predicting the stress state around the tip of the

crack. K depends on the size and location of the crack as well as sample geometry. It

is important that the maximum stress around the tip of the crack not to exceed the

fracture toughness. Otherwise, if K exceeds the fracture toughness values, crack

initiates and propagates.

Formula for calculating the stress intensity factor for beam and plate type geometries

is given below:

𝐾 = 𝜎√𝑎 × 𝜋 × 𝑓(𝑎

𝑤) (2.1)

where:

σ: remote stress applied to component (MPa)

a: crack length (m)

f (a/w): correction factor that depends on specimen and crack geometry

w: specimen width or beam depth (m)

2.2.3. Fracture Toughness

Fracture toughness, KC is the critical value of stress intensity factor that represents the

material’s resistance to fracture. It depending on loading rate, temperature,

environment, composition and microstructure with geometric effects.

The mode I, opening mode, fracture toughness of concrete can be expressed by the

critical stress intensity factor, 𝐾𝐼𝐶. Similarly, especially in concrete related studies, 𝐺𝐶,

energy release rate usually used to express the fracture toughness. The term 𝐺𝑐, called

11

the critical strain energy release rate was generalized by the Irwin who compiled crack

extension related studies and expressed the rate of change in potential energy with

crack area. He indicated that in order to overcome the surface energy of the new cracks

in a fracturing material, the sufficient potential energy must be required. Irwin form

of energy criterion can be written as;

For plane stress;

𝜎 = √𝐸𝐺𝑐

𝜋𝑎 (2.2)

For plane strain;

𝜎 = √𝐸𝐺𝑐

(1−𝜈2)𝜋𝑎 (2.3)

When stress intensity factor reaches its critical value, crack propagation occurs. The

relation between the critical stress intensity factor and critical energy release rate can

be shown as;

For plane stress;

𝐺𝑐 =𝐾𝐶

2

𝐸 (2.4)

12

For plane strain;

𝐺𝐶 = 𝐾𝐶2 (

1−𝜈2

𝐸) (2.5)

GC: Critical energy release rate (MPa.m)

E: Elastic Modulus (MPa)

υ: Poisson’s ratio

KC: Critical stress intensity factor (MPa√m)

2.2.4. Linear Elastic Fracture Mechanics

Linear Elastic Fracture Mechanics works under the assumption of the material being

linear elastic and isotropic. Assuming that the material is linear elastic and isotropic

indicate that the material properties are independent of direction. At the same time,

elastic modulus, E and Poisson’s ratio, υ are two independent elastic constant that

material has. In LEFM assumption, considering the theory of elasticity, the stress field

around the crack tip can be calculated. However, Linear Elastic Fracture Mechanics,

LEFM, is only applicable when the inelastic deformation around the crack path is

relatively smaller compare to the size of a crack.

Irwin found a method for calculating the amount of energy available for fracture.

𝜎𝑖𝑗 = (𝐾𝐼

√2𝜋𝑟)𝑓𝑖𝑗(𝜃) (2.6)

𝜎𝑖𝑗 : Cauchy Stress

𝐾𝐼 : stress intensity factor

r: the distance from the crack tip

13

𝜃 : angle with respect to the plane of the crack

𝑓𝑖𝑗 : function depending on the crack geometry and loading conditions

In general, LEFM is valid when the nonlinear material deformation at the crack tip is

small enough. In order to characterize nonlinear behavior like plastic deformation for

many materials, there was a need for an alternative fracture mechanics model namely

Elastic-Plastic Fracture Mechanics. Unlike LEFM, the material is assumed to be

isotropic and elasto-plastic.

2.3. Fracture Toughness Testing with Flattened Brazilian Disc Test Method

Brazilian tensile strength testing specimen geometry was suggested by Guo et al.

(1993) as a mode I fracture toughness test method so that without machining a notch

or crack, mode I fracture toughness (Kıc) may be determined.

The relation between stress intensity factors (SIF) were studied by Guo et al. (1993).

A formula using dimensionless stress intensity factor, YI and dimensionless crack

length, a/R was derived by numerical integration method. From the numerical

solution, it was found out that dimensionless stress intensity factor could be expressed

as a function of dimensionless crack length.

Changing the loading angles between 5°- 50°, Guo et al., 1993 showed the relationship

between different crack lengths and the stress intensity factors for Flattened Brazilian

Disk type geometry.

After numerical interpretations, formula for BDT under mode I fracture toughness was

derived as follows (Guo et al., 1993):

𝐾𝐼𝐶 = 𝐵 × 𝑃𝑚𝑖𝑛 × 𝑌𝐼(𝑎

𝑅) (2.7)

14

Where:

𝐾𝐼𝐶: mode I fracture toughness

B: the constant dependent on geometry of the specimen

B: 2

√𝑅×𝑡×𝑎×𝜋√𝜋 (2.8)

𝑃𝑚𝑖𝑛: local minimum load

R: disc radius

t: disc thickness

𝑌𝐼(𝑎

𝑅): dimensionless stress intensity factor

a: half of crack length

a/R: dimensionless crack length

Method suggested by Guo et. Al (1993) has some limitations and problematic cases

such as: crack initiation at the center and crack propagation along vertical axis is not

guaranteed, also it could not explain the relation between loading angle and where the

crack initiates (Wang and Xing, 1999). In the problems that crack initiated at the center

inconsistent SIF values resulted due to the assumption of uniform arc loading and

wrong selection of domain, (Figure 2.4).

15

Figure 2.4. The Brazilian Disc specimen under the uniform arc loading (at left) and the Flattened

Brazilian Disc specimen under the uniform diametral compression (at right) (Wang & Wu, 2004)

A better method was proposed Wang and Wu (2004) “for Flattened Brazilian Disc

(FBD) in order to overcome the problems of Brazilian Disc Test (BDT) proposed by

Guo et al. (1993). The geometry suggested for this method replaced opposite curved

surfaces with flattened load application ends of width (2L). This way a simple loading

configuration is provided and crack initiation at the disc center is guaranteed by

discarding crushing problem at contact points. FBD geometry is illustrated in Figure

2.5 where the red solid line demonstrates the location of the crack formation during

loading (2a), red dashed line indicates the crack path and its maximum gives the value

of critical crack length (2ac), orange arc shows the loading angle (2α), black t and 2L

indicate the thickness and flattened end width of the specimen.

16

Figure 2.5. The geometric representation of Flattened Brazilian Disc (Keles and Tutluoglu, 2011)

Formula derived by Wang and Wu (2004) for mode I fracture toughness of FBD

geometry is provided as:

𝐾𝐼𝐶 =𝑃𝑚𝑖𝑛×𝑌𝑚𝑎𝑥

𝑡×√𝑅 (2.9)

Where:

KIC: mode I fracture toughness (MPa√m )

17

Pmin: local minimum load (MN)

𝑌Imax: maximum dimensionless stress intensity factor

R: disc radius (m)

t: disc thickness (m)

In Figure 2.6 a typical load displacement curve of Flattened Brazilian Disc test result

is shown. In this figure, Pmax is represented by letter a and Pmin is represented by letter

b.

Figure 2.6. A typical load displacement curve (Wang and Xing, 1999)

In Figure 2.7 dimensionless stress intensity factor (YI) changing with the

dimensionless crack length (a/R) is shown. Wang and Xing (1999) stated that, when

a/R increasing, YI also increasing up to its maximum value and after that it starts to

18

decrease. When YI reaches its maximum, it is called maximum dimensionless stress

intensity factor at dimensionless critical crack length. In this circumstances,

dimensionless stress intensity factor only depends on the loading angle and it can be

calculated numerically.

Figure 2.7. Maximum dimensionless stress intensity factor represented by Wang and Xing (Wang and

Xing, 1999)

2.4. Fracture Mechanics of Concrete

Beginning of fracture mechanics of concrete was by Kaplan (Kaplan, 1961) who

conducted experiments with four point bending of notched beams at various sizes. His

experiments showed that fracture toughness of concrete beams were changing

depending on their geometry and size. After that Kesler, Naus and Lott (1971) stated

that the LEFM that Kaplan used was inapplicable on concrete structures with sharp

cracks. Walsh’s experimental works supported Kaplan’s findings. (Walsh, 1979). In

the wake of experimental results on notched concrete beams and their relation with

the KC, in order to describe the crack growth on concrete at least two fracture

parameters were needed. In order to understand and model the behavior of concrete,

a major improvement as made in 1976 by Hillerborg, Modeer and Petersson was

19

fictitious crack model. In 1976, Crack band model was proposed by Bazant in order

to explain the fracture process zone on concrete with using the concept of the strain-

softening, (Bazant, 1976). Jenq and Shah (1985) proposed the two-parameter model

which assumed a crack tip singularity in front of the real crack. (Carpinteri, 1984)

described fracture behavior of the concrete by expressing the rate of change of strain

energy density with the crack growth. Two-parameter model was used by Karihaloo

and Nallathambi to propose effective crack model which assumes a sharp crack in

front of the real crack (Karihaloo and Nallathambi, 1989).

Almost all the work summarized is related to the size effect issues in concrete beams.

Concrete and shotcrete are structurally very similar materials; the difference lies in the

application. Testing work here originally involves splitting disc type specimen

geometries for which tensile cracking along the central line is generated by a

compressive at the ends.

21

CHAPTER 3

3. SHOTCRETE MIXTURE SETUP

In early 1900’s the spraying a cement-sand mixture was developed with the trade name

of Gunite and ever since it has been used in the mining industry. However, it took fifty

years to use the same process with a coarse aggregate, now called shotcrete. After that,

shotcrete was used for the first time on a tunnel project in Austria in mid-50’s. it did

not attract much attention for ten years until Burnaby-Vancouver railway tunnel on

the North American continent was under construction. After it was introduced, it

attracted attention in 1967 and several Canadian and American mining firms had

experimented or started to use shotcrete. (Miner, 1973)

The reason why shotcrete is widely used especially in underground works and tunnel

construction as a rock support is due to the continuously developed mining industry

and their constant search for ways and methods to reduce costs at the same time. Thus,

investigation of the fracture properties of all composites (concrete, shotcrete, etc.) that

are used in the underground openings is crucial in order to reach safe working

environment and conduct safe operations in mining and civil engineering industry.

3.1. Shotcrete Mixture Ingredients

The ingredients of shotcrete mixture are Portland cement, aggregate, water and

additives when necessary. In order to get the optimum strength and proper spraying

ability of shotcrete mixture, correct proportions of ingredients and correct

water/cement ratio are essential.

It is known that the water/cement ratio of the shotcrete should be between 0.35-0.50

(M.G. Alexander and R. Heiyantuduwa, 2009). The required 7 days strength of

22

shotcrete is between 25-30 MPa and 28 days strength is 35-40 MPa. In this study

water/cement ratio selected as 0.5. According to the suggested concrete mixture

properties standard TS EN 2016-1, concrete with 0.5 water cement ratio refer to C30

which is the minimum concrete grade for durable and long-lasting structures.

3.1.1. Portland Cement

Portland cement is a binding material produced by pulverizing a small amount of

gypsum along with the Portland cement clinker which is obtained by burning an

appropriate combination of calcareous and clayey materials, (Figure 3.1).

Figure 3.1. Cement

According to the Turkish Standard namely TS EN 197-1, in Turkey, produced cement

are divided into five groups, which are;

23

CEM I; Portland Cement

CEM II; Portland-Composed Cement

CEM III; Blast Furnace Slag Cement

CEM IV; Pozzolanic Cement

CEM V; Composed Cement (Erdoğan, 2013)

The amount of cement usage is directly effective in determining the mechanical

properties, especially strength, of the shotcrete. According to the application area the

amount of cement should be selected. In experimental studies, CEM I 42.5 R was used

in the shotcrete mixture. 42.5 means the 28-day strength of shotcrete should be 42.5

MPa and the R represents high early strength. The cement content of the mixture is in

generally should be between 300-450 kg/m3.

3.1.2. Aggregate

Aggregates are granular materials such as sand, gravel, crushed stone used with

cement and water in concrete construction. Approximately 75% of the

concrete/shotcrete volume is formed by aggregate. In this study, only fine aggregates

from the ready-mixed concrete plant was used for all laboratory experiments because

of the mold dimensions. dmax, the maximum grain size used for the experimental works

was 0.4 mm which is referred to as fine aggregate in the literature, (Figure 3.2).

24

Figure 3.2. Aggregate

According to the TS EN 1097-6 standard the density of aggregate for shotcrete-

concrete type of specimen should be between 2.5-3 g/cm3. Therefore, the pycnometer

test (Figure 3.3) was the precursor test that should be done in order to get specific

gravity of aggregates.

Pycnometer Test method and Calculation;

M1: mass of clean and dry empty pycnometer container

M2: mass of dry soil and pycnometer container together

M3: mass of dry soil and water mix with pycnometer container

M4: mass of pure water and pycnometer container

25

Figure 3.3. Pycnometer tests

The specific gravity of soil is determined using the relation below:

𝑀2−𝑀1

(𝑀2−𝑀1)−(𝑀3−𝑀4) (3.1)

Table 3.1. Pycnometer test parameters

𝑀1

(g)

𝑀2

(g)

𝑀3

(g)

𝑀4

(g)

G (Specific gravity of aggregate)

28.55 34.75 82.49 78.61 2.67

28.55 37.09 83.94 78.61 2.66

28.55 43.59 88.07 78.61 2.69

Average 2.68

26

3.1.3. Water

Water is used for two purposes. One of them is for washing aggregates to be used in

shotcrete, since aggregates may include clay, silt or organic materials that may

decrease surface adherence character of the pieces. The other one is for the preparation

of shotcrete mixture. Water and cement are combined in specified proportions to start

chemical reaction, namely hydration. Water and cement provide the desired

workability as fresh shotcrete mixture, following the washing of aggregate surfaces

and cement grains in the mixing process of shotcrete.

3.1.4. Admixtures/Additives

There are three purpose for using plasticizer, as an additive. The first one is by

reducing the water/cement ratio in the shotcrete mixture, it provides higher strength.

The second one is increasing the workability of fresh concrete without changing the

material quantities or proportion in the mixture. The third one is it provides technical

and economic benefits by keeping the water/cement ratio to be used in the mixture

constant, while reducing the water and cement quantities. The used admixture as

plasticizer is SIKA ViscoCrete Hi-Tech 2001, (Figure 3.4). The amount of plasticizer

should be 1% by weight of the cement amount.

Figure 3.4. Additives

27

3.2. 3D Molds and Recipe for Shotcrete

For fracture toughness testing work special molds of varying diameters were prepared.

SolidWorks software was used for the technical drawings of 3D-molds, (Figure 3.5).

The thickness/radius (t/R ratio) of the specimens was kept constant as 1.3 for all sizes.

Wall thickness and the solidity percentage of the molds were adjusted according to

the changing diameters in order to get high performance like resistance to the repeated

usage, and to prevent any damage to the sample during extraction out of the mold.

Figure 3.5. Drawing of FBD mold in SolidWorks

In Table 3.2, dimensions of the FBD specimens extracted from the 3D molds are

tabulated.

28

Table 3.2. Dimensions of the specimens extracted from the molds

Mold Name Diameter

(mm)

Thickness

(mm)

Height

(mm)

M-1

M-2

100

120

67

80

98

118

M-3 140 94 137

M-4 160 107 157

M-5 180 120 177

M-6 200 133 196

The picture of molds used for the investigation of size effect on fracture toughness test

is shown in Figure 3.6.

Figure 3.6. Used molds with varying diameters 100 mm to 200 mm

The 3D mold of each diameter group has its own mixture recipe which was adjusted

accordingly the volume of each mold and keeping recipe proportions the same. In

general, the recipe for shotcrete is expressed as for volume of 1dm3.

29

Recipe for 0.5 water/cement ratio shotcrete-concrete type of specimens for 1dm3

mixture;

Cement: 300 g

Water: 150 g

Aggregate: 2015 g

Admixture: 3 g

Recipe for all mold diameters were tabulated in Table 3.3 including the recipe for the

mold prepared specially for static deformability and Brazilian disc tests.

Table 3.3. Recipe for all diameters

Ingredient (g) Specimen Diameter (mm)

100 120 140 160 180 200

Cement 180 300 450 600 930 1260

Water 90 150 225 300 465 630

Admixture

(plasticizer) 1.8 3 4.5 6 9.3 12.6

Aggregates 1209 2015 3023 4030 6247 8463

Total Weight (g) 1480.8 2468 3702.5 4936 7651.3 10365.6

3.3. Preparation of Shotcrete Samples

For the preparation of the shotcrete samples, UTEST mixer with almost 10 dm3

capacity with adjustable speed was used, (Figure 3.7).

30

Figure 3.7. UTEST mixer

For the casting procedure, first, aggregate and then cement was put in the mixer and

materials were mixed for 40 seconds at slow speed in dry condition. After that the

liquid mixture was prepared including water and additive in it and poured into the dry

mixture. All materials were mixed at slow speed in first 40 seconds and then mixed

for 40 seconds in fast speed to achieve the homogeneity in the mixture. For each

sample, attention was given for the consistency and the homogeneity of the mixture.

As the shotcrete mixture design was set to the desired composition to get an early

strength, it was poured into molds without wasting any time. Before starting the

casting process, the molds were lubricated with motor oil in order to avoid difficulty

in demolding process, (Figure 3.8).

31

Figure 3.8. Lubrication process

During the casting procedure in order to avoid the air voids, vibration action was

needed and this was performed manually by hand shaking of the mixture in the mold,

(Figure 3.9).

Figure 3.9. Casted Shotcrete

32

Casting process is very important to obtain homogeneity. If the vibration process is

not performed well or nor done at all, layering occurs according to the casting order.

Homogeneity is disrupted by the formation of air voids in the upper side while the

remaining parts are well-settled on the bottom side, (Figure 3.10).

Figure 3.10. Successful and unsuccessful casting products

33

CHAPTER 4

4. TESTING FOR MECHANICAL PROPERTIES OF SHOTCRETE

Preparation of the shotcrete specimens were the first step for the conventional testing

work. Mix design were made according to the concrete-specification, performance,

production and conformity standard namely EN 206. Casting process was carried out

according to the specific geometry requirements of the particular tests. Cylindrical

core samples which had length/diameter of L/D=2.5 and D=70 mm were prepared for

static deformability tests. Cylindrical disc samples with thickness/diameter ratio of

t/D=0.5 were prepared for Brazilian Disc tests from the molds illustrated in Figure 4.1.

Figure 4.1. Prepared molds for conventional testing

34

In Figure 4.2, shotcrete cores taken out of molds are shown. These are seven day-

cured samples.

Figure 4.2. Cylindrical samples taken out of molds for static deformability test

For Static deformability tests and Brazilian Disc tests to obtain tensile strength, MTS

815 testing system was used in loading the specimens. Tests were conducted according

to ISRM suggested procedures summarized given in Ulusay, 2007.

4.1. Static Deformability Test

Young’s Modulus and Poisson’s Ratio of shotcrete specimens were measured by the

static deformability test that ISRM (1979) suggested. Tests were performed on five

seven day-cured shotcrete specimens by using MTS 815 servo-controlled loading

machine. Two MTS external displacement transducers (having 10 mm capacity with

±0.005 mm accuracy) were mounted on the specimens to measure longitudinal strain.

35

An Epsilon circumferential extensometer was attached to measure lateral strain and to

determine Poisson’s Ratio, (Figure 4.3). To measure UCS results also, samples were

kept under continuing compressive loading until failure.

Figure 4.3. Static Deformability Test Setup

During displacement-controlled testing, rate was kept constant at 0.005mm/s. Data

acquisition frequency was kept as 8Hz. A typical test took about 15 minutes to be

completed.

Results of static deformability tests are tabulated in Table 4.1.

36

Table 4.1. Static deformability test results

Specimen

Length

(mm)

Diameter

(mm)

UCS

(MPa)

Elastic

Modulus

(GPa)

Poisson's

Ratio

S_SD_1 177.5 71.4 25.9 20.03 0.18

S_SD_2 176.0 70.4 22.9 20.64 0.17

S_SD_3 173.5 71.0 29.7 20.96 0.18

S_SD_4 175.0 71.1 29.5 21.59 0.20

S_SD_5 175.0 70.4 24.8 23.81 0.18

Average

175.40 70.9 26.6±3.0 21.41±1.46 0.18±0.01

Average Uniaxial Compressive Strength (UCS) was calculated as 27 MPa. Elastic

Modulus (E) and Poisson’s Ratio (υ) were calculated as 21 GPa and 0.18, respectively.

A typical lateral strain- axial strain curve and stress-strain curve for shotcrete core

specimen are shown in Table 4.4 and Table 4.5, respectively.

37

Figure 4.4. Lateral strain vs axial strain graph

Figure 4.5. Stress vs lateral strain and axial strain graph

38

Test results presented in Table 4.1 are compared to some results reported in literature

to assess the representative shotcrete quality of the mixture used here.

The pioneers of studying mechanical properties of early age shotcrete was Huber

(Schutz, 2010). Including their experimental work and other researchers, changing the

Young’s modulus with time was compiled by Chang, 1994 in Figure 4.6. Elastic

Modulus of seven day-cured shotcrete samples with the mixture in this work,

E=21GPa, is compatible with the results in literature, (Figure 4.6).

Figure 4.6. Development of Young’s modulus with early age of shotcrete compiled from various

research by (Chang, 1994)

In literature, the development of the UCS of early age concrete is available for both

dry and wet mix shotcrete. In Figure 4.7, UCS results of various researchers are

compiled by Chang, 1994. It is known that the mix design and the application

39

technique of the mixture have a great influence on the strength results. So, it is difficult

to know the exact strength at a certain shotcrete age. It is necessary to validate the

results with some preliminary experiments first. Uniaxial compressive strength of

seven day-cured shotcrete samples with mixture recipe of this work yielded UCS=26.6

MPa. This is compatible with the results in literature, (Figure 4.7).

Figure 4.7. UCS results of various researchers compiled by Chang (1994)

In literature, the required 7 days strength of the shotcrete is approximately 25-30 MPa.

According to the suggested concrete mixture properties of standard TS EN 206-1,

concrete with a water/cement ratio of 0.5 is classified as C30 and its 28-day strength

is around 30 MPa for a characteristic cylinder sample. The static deformability tests

showed that the 28-day strength was gained in 7 days to a great extent, this supports

40

the compatibility of the mixture prepared here to represent the shotcrete which is

aimed to provide high-early strength.

Experimental work related to the Poisson’s ratio of early age shotcrete is limited.

Neville (1981) stated that Poisson’s ratio of concrete should be 0.11 to 0.21.

According to Byfors (1980), development of the Poisson’s ratio with time depended

on the quantity and type of aggregates used for the mixture of shotcrete. Aydan, Sezaki

and Kawamoto (1992) conducted experiments to identify the behavior of Poisson’s

ratio with time. Results of their experiments showed that after three days the Poisson’s

ratio of shotcrete was almost fixed at the value of 0.18. In Figure 4.8, corresponding

test results are shown.

Figure 4.8. Variation of Poisson’s ratio with time (Aydan et al., 1992)

41

Equation derive from this work is given as:

𝜐 = 0.18 + 0.32 𝑒−5.6𝑡𝑐 (4.1)

Where tc is the curing time in days.

According to the static deformability test results, Poisson’s ratio (υ=0.18) of seven

day-cured samples here is compatible with the results of Aydan et al. (1992) as

illustrated in Figure 4.8.

4.2. Indirect Tensile Strength Test (Brazilian Disc Test)

In order to calculate the tensile strength of rocks and concrete materials, The Brazilian

Disc Test is preferred since it is a convenient and easy method. In 1978, it was

officially proposed by the International Society for Rock Mechanics (ISRM) for the

rock materials. Since concrete and rock have the same mechanics properties, their

mechanical properties test method can be reference each other. Standardization of this

test method for obtaining the tensile strength of concrete specimens by both the

American Society for Testing and Materials (ASTM) and European Committee for

Standardization.

Indirect Tensile Strength tests were conducted according to the ISRM (1979)

suggested method. These tests were performed on five shotcrete specimens. MTS 815

servo-controlled loading machine was used with constant displacement rate of

0.005mm/s and 8Hz data acquisition frequency. In order to eliminate infinite

compressive stress concentration at loading ends, jaws were used during the tests,

(Figure 4.9).

42

Figure 4.9. Brazilian Disc Test set up

In Table 4.2, Brazilian disc test results including peak loads and calculated tensile

strengths were tabulated, (Table 4.2). Diameter and thickness of all Brazilian Disc

specimens were around 71mm and 33 mm, respectively,

Table 4.2. Brazilian disc test results

Specimen

Name

Peak Load

(kN)

𝜎𝑡

(MPa)

S_BD_1 16.60 4.30

S_BD_2 17.89 4.60

S_BD_3 15.59 4.03

S_BD_4 14.45 3.66

S_BD_5 10.50 3.53

Average 15.01±2.82 4.02±0.44

43

According to the test results, the average peak load was 15 kN, and the average tensile

strength was calculated as σt = 4 MPa.

A typical Brazilian Disc Test sample namely S_BD_2 with central crack clearly

visible is shown in Figure 4.10.

Figure 4.10. A typical Brazilian Disc sample with central crack clearly visible

A typical force-displacement curve of the same specimen namely S_BD_2 during the

Indirect Tensile Strength Test with Brazilian Disc geometry is shown Figure 4.11.

44

Figure 4.11. Force-Displacement curve of a Brazilian Disc test specimen

It should be noted that load-displacement curve has a local minimum load (Pmin) point

similar to those observed in FBD fracture toughness tests. This is believed to be caused

by the use of jaws on the upper and lower loading boundaries of the discs. The use of

jaws is distributing the line load and artificially imposing a loading angle which is

estimated to be around 20°.

4.3. Tensile Strength Estimation from Brazilian Disc Tests

Cementitious materials like concrete generally exhibit high compressive strength, low

tensile strength, and brittle failure under tensile loading. So, in order to avoid local

collapse or failure on the structure because of this weakness and the consequences of

the stress distributions related to it, determination of the tensile strength of concrete is

as an important parameter related the structure design of concrete work. (Liang & Tao,

2014)

45

It is possible to estimate tensile strength from FBD tests. Pmax values before the load

drop can be used in some recently developed expressions to compute tensile strength.

There are two well-known formulations for this purpose one is by Wang and the other

one is Keles and Tutluoglu. These are explained below.

4.3.1. Wang’s Approach

By assuming that the specimen is under uniformly distributed tensile stress, in 1953

Carneiro and Barcellos stated that the tensile strength can be expressed as:

𝜎𝑡 =2𝑃𝑚𝑎𝑥

𝜋𝐷𝑡 (4.2)

Where 𝜎𝑇 is tensile strength, 𝑃𝑚𝑎𝑥 is the failure load of the specimen, D is the diameter

of the specimen, t is the thickness of the specimen, (Japaridze, 2015).

However, the Brazilian test has the disadvantage that high shear stresses are induced

close to the loading platens apart from the tensile stresses, which are developed in the

disc. Wang and Xing (1999) introduced two mutually parallel planes to be used as

surface loading application to the disc. Parallel loading ends are used to distribute the

concentrated load. Griffith strength criterion (Griffith, 1924) was applied by Wang

and Xing (1999); Wang and Wu (2004); Wang, Jia, Kou, Zhang and Lindqvist

(2004a); Kaklis, Agioutantis, Sarris and Pateli (2005) and Keles & Tutluoglu (2011)

to develop an analytical formula to calculate the tensile strength in Flattened Brazilian

Disc.

According to the Griffith’s theory to form cracks at the center in regular Brazilian test

stress conditions required are;

3𝜎1 + 𝜎3 = 0 Which yields, 𝜎𝐺 = 2𝑃

𝜋𝐷𝑡 (4.3)

46

Where 𝜎1 and 𝜎3 are maximum principle stress and minimum principle stress,

respectively at the center. 𝜎𝐺 = 𝜎𝜃 at the same time.

The failure occurs, 𝜎𝑡 = 𝜎𝐺 where 𝜎𝐺the equivalent stress is, and it was based on the

principle stresses 𝜎1 maximum and 𝜎3 minimum and if the tensile stress is considered

positive:

If 3𝜎1 + 𝜎3 ≥ 0 , then 𝜎1 = 𝜎𝑡 (4.4)

If 3𝜎1 + 𝜎3 < 0 , then 𝜎𝐺 = 𝜎𝑡 = −(𝜎1−𝜎3)2

8(𝜎1+𝜎3) (4.5)

In cylindrical system, the stress inside the sample can be expressed by 𝜎𝜃 and 𝜎𝑟

.Wang et al. (2004) assumed that there is no shear stress in the direction of 𝜎𝜃 and 𝜎𝑟.

Timoshenko and Goodier (1970) stated that when a Brazilian disc is subjected to a

radial compressive force, the stress solution on the loading diameter can be expressed

as:

𝜎𝜃 =2𝑃

𝜋𝐷𝑡 (4.6)

𝜎𝑟 =2𝑃

𝜋𝐷𝑡 (1 −

4𝐷2

𝐷2−4𝑟2) (4.7)

When the Brazilian Disc is flattened loading angle comes into the problem. Wang et

al. (2004) analyzed the crack initiation condition at the center and they stated that

when 2α is equal or larger than 20°, the primary tensile crack will initiate at the center

and 𝜎𝐺 must reach a maximum value at that point.

Thus, for the Flattened Brazilian Disc at the center of disc;

47

(𝜎𝑟−𝜎𝜃)2

8(𝜎𝑟+𝜎𝜃)= 𝜎𝐺 = 𝜎𝑡 (4.8)

To determine 𝜎𝑇, Wang et al. (2004) derived approximate formulae for 𝜎𝜃 and 𝜎𝑟 and

they assumed that the crack initiates at the specimen center, (Figure 4.12).

Figure 4.12. Specimen subjected to a uniform diametric loading (Wang et al.,2004)

𝜎𝜃 = −2𝑃

𝜋𝐷𝑡 𝑐𝑜𝑠3𝛼

𝛼

𝑠𝑖𝑛𝛼 (4.9)

𝜎𝑟 =2𝑃

𝜋𝐷𝑡 (𝑐𝑜𝑠3𝛼 + 𝑐𝑜𝑠𝛼 +

𝑠𝑖𝑛𝛼

𝛼)

𝛼

𝑠𝑖𝑛𝛼 (4.10)

Wang et al. (2004) expressed 𝜎𝑡 as:

𝜎𝑡 =2𝑃

𝜋𝐷𝑡[

(2𝑐𝑜𝑠3𝛼+𝑐𝑜𝑠𝛼+𝑠𝑖𝑛𝛼𝑠⁄ )

2

8(𝑐𝑜𝑠𝛼+𝑠𝑖𝑛𝛼𝛼⁄ )

𝛼

𝑠𝑖𝑛𝛼] (4.11)

k

48

So, In Flattened Brazilian Disc, a dimensionless correction coefficient k is joined to

the equation to determine tensile strength formula.

𝜎𝑡 = 𝑘2𝑃𝑚𝑎𝑥

𝜋𝐷𝑡 (4.12)

In order to get tensile strength from flattened Brazilian disc geometry, correction

coefficient k is calculated from Wang’s equation for loading angle of 2α=22° (0.19

radian) and the result was equal to k= 0.9522.

By using k into the equation and also Flattened Brazilian disc specimens’ failure loads

(Pmax), diameters (D), thickness (t), indirect tensile strength for changing diameters

between 100 mm to 200mm at constant loading angle was calculated. In Table 4.3,

calculated tensile strength and the geometric parameters of the specimens were

tabulated. The tensile strength values computed as the average of five tests.

Table 4.3. Average tensile strength from Wang’s correction coefficient

Group

Name

Dave

(mm)

tave

(mm)

Pmax ave

(kN)

𝜎𝑡 𝑊

(MPa)

S100 99.0 66.62 24.98 2.30

S120 118.5 79.55 37.31 2.40

S140 138.4 83.99 45.77 2.39

S160 158.1 103.86 67.68 2.50

S180 174.4 122.38 102.92 2.87

S200 197.6 133.16 127.14 2.93

∗ 𝜎𝑡 𝑊 represents calculated tensile strength by using Wang’s correction coefficient.

The change in tensile strength with the specimen diameter is shown in Figure 4.13.

Tensile strength increases with sample size following a fitted third degree polynomial.

The lowest 2.30 for 100 mm size group and the highest is 2.87 for the 200 mm group.

49

Figure 4.13. Tensile strength versus specimen diameter using Wang approach

A third-degree polynomial functional fit to the data points in Figure 4.13 is the best fit

and this fitted function gives an estimated maximum at D=0.247m as the 𝜎𝑡= 3.20

MPa. With conventional Brazilian disc tests using curved jaws, tensile strength of

shotcrete was measured as 4.02 MPa. The ratio of the tensile strength obtained from

the FBD test and the regular BD test is showed Figure 4.14.

50

Figure 4.14. The ratio of the tensile strengths from FBD and BD with varying diameter

A third degree polynomial functional fit to the ratios in Figure 4.14 is the best fit and

this fitted function gives an estimated maximum at D=0.247m as the ratio=0.796.

According to the extreme points of the equation, when diameter increases, the ratio

approach one but can’t reach it. This can be explained as; the loading angle imposed

by the curved jaws used in the regular Brazilian Disc Test is possibly lower than the

loading angle of the Flattened Brazilian Disc Test (2α=22°).

4.3.2. Keles and Tutluoglu’s Approach

Similar work conducted by Keles and Tutluoglu (2011). They stated that in their

numerical analysis, when 2α was changed between 15° and 60° crack was initiate at

the center and they determined the principle stresses to calculate tensile strength 𝜎𝑡.

For each 2α dimensionless principle stresses at the center calculated and formulized

as;

51

�̅�1 =𝜎1

2𝑃𝜋𝐷𝑡⁄

= 1.08𝑐𝑜𝑠𝛼 + 1.92 (4.13)

�̅�3 =𝜎3


= −0.94𝑐𝑜𝑠𝛼 − 0.04 (4.14)

And substituting into equation:

𝜎𝐺 = 𝜎𝑡 = −(𝜎1−𝜎3)2

8(𝜎1+𝜎3) ; (4.15)

�̅�𝐺 =𝜎𝐺


= 0.83𝑐𝑜𝑠𝛼 + 0.15 (4.16)

In fact, the coefficient defined by (Keles & Tutluoglu, 2011), �̅�𝐺, is the same

coefficient k as defined by Wang and Wu (2004) but different form of expression.

According to the equation determined by Keles, k is now calculated as k=0.9648.

𝜎𝑇 =2𝑃

𝜋𝐷𝑡[0.83𝑐𝑜𝑠𝛼 + 0.15] (4.17)

�̅�𝐺 (Namely k in Wang’s approach)

This time by using Keles’s correction coefficient into the equation and also Flattened

Brazilian disc specimens’ failure loads (Pmax), diameters (D), thickness (t) indirect

tensile strength for changing diameters between 100mm to 200mm at constant loading

angle were calculated. In Table 4.4 calculated tensile strength and the parameters used

were tabulated.

52

Table 4.4. Tensile strength calculation from Keles and Tutluoglu’s correction coefficient

Group

Name

Dave

(mm)

tave

(mm)

Pmax

(kN)

𝜎𝑡 𝐾 𝑇

(MPa)

S100 99.0 66.62 24.98 2.33

S120 118.5 79.55 37.31 2.43

S140 138.4 83.99 45.77 2.42

S160 158.1 103.86 67.68 2.53

S180 174.4 122.38 102.92 2.91

S200 197.6 133.16 127.14 2.97

∗ 𝜎 𝑡 𝐾 𝑇 represents calculated tensile strength by using Keles and Tutluoglu’s correction coefficient.

Calculated tensile strength according to the corresponding diameters were shown in

Figure 4.15. Tensile strength increases with sample size following a fitted third degree

polynomial. The lowest 2.33 MPa for 100 mm size group and the highest is 2.97 MPa

for the 200 mm group.

Figure 4.15. Tensile strength versus specimen diameter using Keles and Tutluoglu approach

53

A third-degree polynomial functional fit to the data points in Figure 4.15 is the best fit

and this fitted function gives an estimated maximum at D=0.247 m as the ratio=3.24.

In Brazilian disc test experimentally calculated tensile strength of shotcrete was

obtained as 4.02 MPa. Changing difference between obtained tensile strength from

Brazilian Disc test and Fattened Brazilian disc test method according to the testing

diameters were presented in Figure 4.16.

Figure 4.16. The ratio of tensile strengths from FBD and BD with related diameters

A third degree polynomial functional fit to the ratios in Figure 4.16 is the best fit and

this fitted function gives an estimated maximum at D=0.247m as the ratio=0.806.

According to the extreme points of the equation, when diameter increases, the ratio

approach one but can’t reach. This can be explained as; the loading angle imposed by

the curved jaws used in the regular Brazilian Disc Test is possibly lower than the

loading angle of the Flattened Brazilian Disc Test (2α=22°).

54

Figure 4.17. Bazant’s size effect investigation (Bazant et al., 1991)

According to Bazant's study, for the small sizes, the Brazilian Disc strength decreased

with increasing size until a certain diameter. As a result of experiments applied in

concrete while diameter of the specimen changed from 10 to 508 mm, threshold

diameter was around 200 mm. After that certain diameter, strength increased in direct

proportion. In this study, for the shotcrete specimens that had 0.5 water/cement ratio,

the increasing behavior of tensile with diameter was observed between 100 mm

diameter and 200 mm diameter.

55

CHAPTER 5

5. MODE I FRACTURE TOUGHNESS TESTS

Understanding the fracture mechanism is crucial to solve many engineering problems.

In order to be able to investigate the conditions of the fracture growth, measurement

of toughness is required for fracture analysis.

When considered the other testing methods, Flattened Brazilian Disc Test method has

been preferred testing method for determination of the fracture toughness due to the

relatively easiness for the specimen preparation, compressive load application on the

flat ends and also simple testing procedure.

For fracture toughness testing, FBD method with flat compressive load application

boundaries is the simplest method among the other methods considering specimen

preparation, loading type, and testing procedures.

Objective of this work is to study the variation fracture toughness of shotcrete with

specimen size and curing time. 30 experiments were performed to investigate the size

effect on mode I fracture toughness and 21 experiments were performed to investigate

the effect of curing time on mode I fracture toughness.

5.1. Fracture Toughness Testing Work

Before conducting the experiments, dimensions of the specimens were measured since

all of the specimens differed slightly due to the imperfections of casting process.

Shotcrete specimens were prepared with six different diameters which are 100 mm,

120 mm, 140 mm, 160 mm, 180 mm, and 200 mm.

56

In the second part of the experimental program effect of curing time on KIC was

investigated by varying the curing time tc as 1 day, 2 days, 3 days, 5 days and 7 days.

For a specific diameter of 160 mm, they were grouped depending on the five curing

time levels in order to investigate the curing time effect on the fracture toughness of

the shotcrete.

During all the tests, specimens were loaded using the MTS 815 servo-controlled

loading machine with a constant displacement rate of 0.0004 mm/s and 8Hz data

acquisition frequency.

In all fracture toughness testing work, loading angle 2α of the specimens is kept nearly

as 22° which corresponds to flattened end/radius ratio of L/R=0.19.

When the experiment started, load gradually increased up to a maximum point, Pmax

at which an unstable crack initiated at the center of the specimen. At this stage, a

sudden drop in load from Pmax to local minimum, Pmin occurred. Local minimum

point, Pmin was the turning point between unstable and to stable crack propagation.

Stable crack growth started at the Pmin. At this load, experimental critical crack length

(ace) was measured. Close-up photos were taken in order to measure the critical crack

lengths through Adobe Photoshop Program. The purpose was the comparison between

experimental and numeric critical crack lengths. Specimen dimensions, Pmax, Pmin and

experimental critical crack length were recorded for each test. The average of the

recorded Pmax values of each testing group was used for the tensile strength

computations from FBD geometry with the help of two researcher’s approaches.

A typical force-displacement curve related the Mode I Fracture Toughness Test with

Flattened Brazilian Disc geometry is shown Figure 5.1.

57

Figure 5.1. A typical Force-Displacement curve of a Flattened Brazilian Disc test

According to the Wang and Wu (2004), the last discussion was about the validity of a

FBD test. To be valid, the failure must be caused by the development of the primary

crack, not the secondary ones. In a typical force displacement graph of the test results,

when the load reaches the maximum (Pmax) at the end of elastic deformation, and local

minimum load (Pmin) is reached when the primary cracks propagate till its critical

length. Second increase in load must be observed to progress up to a load level which

is supposed to be lower than Pmax. The load increase in the second rise should never

be greater than the first one, (Figure 5.1). Otherwise, the secondary cracks would play

role in the failure and disc may be split into more pieces than it should be. This

criterion was taken into consideration in all the testing work here.

58

A typical experimental critical crack length measurement related the Mode I Fracture

Toughness Test with Flattened Brazilian Disc geometry is shown Figure 5.2.

Figure 5.2. A typical experimental critical crack length measurement

5.2. Computation for Fracture Toughness

For determining the mode I fracture toughness value for FBD testing method was

calculated by using the Eq. 5.1 (Wang and Xing, 1999).

𝐾𝐼𝑐 =𝑌𝐼𝑚𝑎𝑥 𝑃𝑚𝑖𝑛

𝑡 √𝑅 (5.1)

Where,

𝐾𝐼𝑐 : Fracture toughness (MPa√𝑚)

Pmin : Minimum local load (kN)

59

R : Specimen Radius (mm)

t : Specimen thickness (mm)

𝑌𝐼𝑚𝑎𝑥 : Maximum dimensionless stress intensity factor (SIF) which is determined

from numerical modeling.

Özdoğan (2017) developed a formula based on numerical analysis for determination

of the critical crack length and the maximum dimensionless stress intensity factor at

the onset of stable crack propagation or at the local minimum points depending on the

loading angle. The J-integral approach was used for KI computation in ABAQUS

models.

Özdoğan followed a procedure that numerical FBD models were developed based on

different dimensionless crack lengths (a/R) for each loading angle in order to find KI

values. The KI values obtained from these models were converted into YI values by

using the equation described by Wang and Xing (1999) as follows;

𝑌𝐼 =𝐾𝐼 𝑡 √𝑅

𝑃 (5.2)

Between the range of loading angles 2 to 50, numerical models of FBD were created

based on different dimensionless crack lengths (a/R) in order to find mode I stress

intensity factor (KI) values. KI values from the ABAQUS were used to calculate

dimensionless stress intensity factor YI by Wang’s formula. For each loading angle,

a/R depended YI values were fitted graphs and YImax values were generated by using

statistical program packages. There were two equations generated; one was for finding

YImax values for each loading angle, (Özdoğan,2017):

𝑌𝐼𝑚𝑎𝑥= 𝑒

1.6897+1.4854∗(2)−62.3324∗(2)2

1+31.7876∗(2)+4.3693∗(2)2−2.1703∗(2)3 (5.3)

60

In the Eq. (5.3), YImax represents maximum mode I dimensionless stress intensity factor

(SIF) and 2α is loading angle in radians.

The second equation fitted on acn/R vs loading angle (2α) plot and generated a formula

given in Eq. (5.4), (Özdoğan,2017):

𝑎𝑐𝑛𝑅⁄ =0.9974*e-0.844*(2) (5.4)

In Eq. (5.4), loading angle, 2α is in radians.

According to Özdoğan (2017), these equations are valid and reliable for loading angles

(2α) between 2 to 50. However, while working on the Brazilian test theoretically,

experimentally and numerically the validity of such tests needed to be investigated by

paying attention to the crack initiation location. In literature, there were many

investigations of the stress analyses for crack initiation location on Brazilian disc such

as studies of Wang and Xing (1999); Wang and Wu (2004); Wang et al. (2004a);

Kaklis et al. (2005) and Keles and Tutluoglu (2011). By using boundary element

method, critical 2α was found to be greater than 19.5° (Wang and Xing 1999). This

angle was found to be equal to 20° and Wang and Wu (2004) and Wang et al. (2004a),

reported that the upper limit for this angle should not be too large. It was 15° in Kaklis

et al. (2005) while it was between 15° to 60° in Keles and Tutluoglu (2011) by finite

element methods.

Considering the suggestions in the literature and practicality of constructing molds,

loading angle 2α was selected as 22° in current work, so that crack is expected to

initiate and develop along the central path.

According to the selected loading angle 2α=22° which was 0.384 in radians

corresponding YImax was calculated mathematically as 0.604 for all diameters.

61

After finding YImax for tested specimens numerically, for determining the mode I

fracture toughness value for FBD testing method was calculated by using the Eq. (5.5)

𝐾𝐼𝑐 =𝑌𝐼𝑚𝑎𝑥 𝑃𝑚𝑖𝑛

𝑡 √𝑅 (5.5)

For loading angle of 22° (0.384 in radians), corresponding acn/R was calculated

mathematically as 0.721. For each sample diameter, the measured critical crack length

at the local minimum point and numerically computed critical crack length for 2α=22°

loading angle were compared in proceeding sections.

5.3. Investigation of Size Effect on Mode I Fracture Toughness of Shotcrete

Size effect is an important characteristic of the fracture behavior in quasi brittle

materials such as concretes, rocks and ceramics. The strength and toughness of

specimens or structures made of these materials depends on their size thus especially

in the field of engineering applications, using fracture mechanics is the most

challenging concept to investigate.

The size effect was described as the geometrically similar structures have different

nominal stress with respect to varying sizes. Perdikaris, Calomino and Chudnovsky

(1986) indicated that the observed size effect on the fracture toughness in the static

and fatigue tests suggested that GIC and KIC cannot be considered to be material

parameters, (Perdikaris, 1986).

Bazant et al. (1991) conducted experimental studies to investigate the size effect on

Brazilian concrete specimens and he deduced that up to a certain critical diameter, size

effect existed and crack length expanded.

62

In this study while working with specimen size, loading angle kept constant at 22° in

order to observe the effect of different diameters on mode I fracture toughness.

Shotcrete-concrete FBD testing specimens were prepared according to six different

diameters which are 100 mm, 120 mm, 140 mm, 160 mm, 180 mm, and 200 mm. A

total of 30 experiments were performed to investigate the size effect on mode I fracture

toughness; that is approximately 5 experiments of each diameter group.

Test specimens’ name code was explained below Figure 5.3. Code includes type of

specimen, sample diameter (D), and the number of testing specimen, (Figure 5.3).

Figure 5.3. Name code of tested FBD specimens

A typical Flattened Brazilian Disc Test geometry with generalized dimensions was

shown in Figure 5.4 .

63

Figure 5.4. FBD specimen geometry

General geometric entities of the diameter-based specimen groups related to their

codes are given in Table 5.1.

Table 5.1. Dimensions of shotcrete specimens

Name D (mm) 2L(mm) t (mm)

S100 100 19 67

S120 120 23 80

S140 140 27 84

S160 160 31 104

S180 180 34 122

S200 200 38 133

64

5.3.1. Tables for Individual Fracture Toughness Test Results

Individual test results are presented in Tables 5.2 to 5.7 for the seven day-cured

samples of 100 mm, 120 mm, 140 mm, 160 mm, 180 mm and 200 mm diameter

groups.

Table 5.2. t, 2ace, ace/R, Pmin, and KIC values of FBD specimens having 100 mm diameter

Name t(mm) 2ace(mm) ace/R Pmin(kN) 𝐾𝐼𝐶(𝑀𝑃𝑎√𝑚 )

S100_s1 66.1 71.3 0.720 24.63 1.01

S100_s2 66.0 71.6 0.723 25.03 1.03

S100_s3 71.9 71.5 0.723 20.15 0.76

S100_s4 67.2 71.6 0.723 21.98 0.89

S100_s5 62.1 71.5 0.722 21.94 0.96

Average 71.5±0.12 22.75±2.05 0.93±0.11



S120_s1 80.5 84.4 0.712 32.34 1.00

S120_s2 81.7 84.8 0.716 32.64 0.99

S120_s3 79.2 85.1 0.716 28.13 0.88

S120_s4 79.1 86.3 0.730 34.43 1.08

S120_s5 79.1 86.5 0.730 27.40 0.86

S120_s6 77.7 86.3 0.730 33.71 1.08

Average 85.6±0.91 31.44±2.95 0.98±0.09



S140_s1 77.9 100.6 0.727 37.14 1.09

S140_s2 80.2 102.2 0.736 38.65 1.11

S140_s3 94.3 101.9 0.738 47.47 1.16

S140_s4 78.5 99.5 0.719 32.65 0.96

S140_s5 89.1 101.0 0.731 38.99 1.01

Average 101.0±1.08 38.98±5.38 1.06±0.08

65



S160_s1 104.3 114.1 0.722 57.85 1.19

S160_s2 105.4 115.7 0.732 57.04 1.16

S160_s3 104.9 114.4 0.722 56.28 1.15

S160_s4 102.0 116.0 0.734 57.96 1.22

S160_s5 102.8 115.5 0.729 56.54 1.18

Average 115.1±0.84 57.13±0.76 1.18±0.03



S180_s1 121.7 130.8 0.743 85.69 1.43

S180_s2 124.1 129.2 0.726 88.00 1.44

S180_s3 123.4 131.4 0.739 88.83 1.46

S180_s4 123.1 131.5 0.739 88.71 1.46

S180_s5 119.6 131.2 0.741 81.20 1.38

Average 130.8±0.94 86.49±3.21 1.43±0.03



S200_s1 136.7 150.4 0.760 114.11 1.60

S200_s2 132.0 147.8 0.748 97.18 1.42

S200_s3 131.9 149.3 0.756 95.81 1.40

S200_s4 132.0 148.4 0.751 99.28 1.45

Average 149.0±1.13 101.60±8.46 1.46±0.09

KIC is seen to increase significantly with specimen size. The increase in KIC is almost

57% from 100 mm to 200 mm.

66

5.4. Investigation of Curing Time on Mode I Fracture Toughness of

Shotcrete/Concrete Type of Specimen

In order to investigate the effects of curing time on fracture toughness of shotcrete-

concrete type of specimen, 1 day, 2 days, 3 days, 5 days and 7 days air-cured shotcrete

specimens were tested. Diameter and the loading angle was kept constant at 160 mm

and 22°, respectively. A total of 21 experiment results were investigated to analyze

the effect of curing time on mode I fracture toughness of shotcrete specimens. For

each curing time investigation group, four tests were conducted.

It can be discussed that the crack propagation mechanism developed for mature

concrete can be applied to the early aged concrete (Hillerborg et al., 1976; Bazant,

2002). However, process of propagation cannot be fully explained by using this

approach. (Dao, Dux, and Morris, 2014).

Test specimens’ name code was explained below Figure 5.3. Code includes type of

specimen, sample diameter (D), curing time (day) and the number of testing specimen,

(Figure 5.5).

Figure 5.5. Name code of tested FBD specimens

67

5.4.1. Tables of Results for Curing Time Investigation

In Tables 5.8 to 5.12, KIC values are listed for 1 day, 2 day, 3 day, 5 day and 7 day air-

cured of 160 mm diameter samples. For seven-day cured 160 mm diameter group,

additional result was available from the size effect study.

Table 5.8. t, Pmin, and KIC values of FBD specimens having 160 mm diameter with 1 day cured

Name t(mm) Pmin(kN) 𝐾𝐼𝐶(𝑀𝑃𝑎√𝑚 )

S160-1D-s1 103.8 33.20 0.69

S160-1D-s2 104.7 29.42 0.60

S160-1D-s3 104.3 31.38 0.65

S1601-D-s5 104.0 33.29 0.69

Average 31.82±1.83 0.66±0.04

Table 5.9. t, Pmin, and KIC values of FBD specimens having 160 mm diameter with 2 days cured


S160-2D-s1 104.0 37.28 0.77

S160-2D-s2 105.0 42.28 0.87

S160-2D-s3 104.4 36.36 0.75

S160-2D-s4 103.0 38.85 0.81

Average 38.69±2.60 0.80±0.05



S160-3D-s1 103.9 38.60 0.80

S160-3D-s2 104.5 39.94 0.82

S160-3D-s3 103.8 42.28 0.88

S160-3D-s4 104.0 40.80 0.84

Average 40.41±1.54 0.83±0.03

68



S160-5D-s1 105.0 56.51 1.15

S160-5D-s2 104.8 55.83 1.14

S160-5D-s3 104.0 48.67 1.01

S160-5D-s3 104.0 51.12 1.06

Average 53.03±3.77 1.09±0.07



S160-7D-s1 104.3 57.85 1.19

S160-7D-s2 105.4 57.04 1.16

S160-7D-s3 104.9 56.28 1.15

S160-7D-s4 102.0 57.96 1.22

S160-7D-s5 102.8 56.54 1.18

Average 57.13±0.76 1.18±0.03

KIC is seen to increase significantly with curing time, especially at early curing stages.

The increase in KIC is almost 100% from one day to seven-day curing states.

69

CHAPTER 6

6. EXPERIMENTAL RESULTS AND DISCUSSION

Tests with Flattened Brazilian Disc geometry were carried out to detect the presence

of size effect on mode I fracture toughness. During the tests critical crack lengths at

which a stable crack starts to propagate were measured.

30 shotcrete specimens, curing time of seven days, were subjected to mode I fracture

toughness test with varying diameters between 100 mm and 200 mm. This was done

to monitor the effect of changing diameter or in other words specimen size effect on

mode I fracture toughness. For each diameter group around five tests were conducted

and one average fracture toughness was evaluated. Loading angle was kept constant

at 22°.

In the ground control system, shotcrete is used to provide temporary surface control

for local stability before the primary support is installed. Because the shotcrete must

become self-supporting before miners and equipment can work safely underneath, the

curing characteristics of the shotcrete are critical to the speed of the mining cycle.

Surface defects and cracks may already exist or may develop in shotcrete at ages from

several hours after casting. These cracks may affect the service life of shotcrete by

propagating or they can cause much damage either economically or even worst fatal.

Therefore, it is important to understand the underlying fracture mechanism changing

with curing time.

Early-age developed 21 shotcrete specimens with constant diameter D=160 mm and

constant loading angle (2a=22°) with 1 day, 2 days, 3 days, 5 days and 7 days cured

shotcrete specimens were subjected to mode I fracture toughness test in order to

determine the effect of curing time on mode I fracture toughness. For each curing time

group around four tests were conducted and one fracture toughness was evaluated.

70

6.1. Tables of Results for Size Effect Investigation

Seven-day air-cured shotcrete specimens with Uniaxial Compressive Strength (UCS)

of 27 MPa, Elastic Modulus (E) of 21 GPa, and Poisson’s Ratio (υ) of 0.18 results in

fracture toughness values ranging between 0.93-1.46 MPa√𝑚 for varying diameters.

In Table5.1, diameter of specimens, average local minimum loads (Pmin), average

critical crack lengths (2ace) and mode I fracture toughness values (KIC) were listed for

7 day cured shotcrete specimens. Overall test results are tabulated in Table 6.1 and

individual group averages are presented in Table 6.2.

71

Table 6.1. All test results for investigation of size effect on the fracture toughness

Name Pmin(kN) 2ace(mm) ace/R KIC (MPa√𝑚)

S100_s1 24.63 71.30 0.72 1.01

S100_s2 25.03 71.60 0.72 1.03

S100_s3 20.15 71.50 0.72 0.76

S100_s4 21.98 71.60 0.72 0.89

S100_s5 21.94 71.50 0.72 0.96

S120_s1 32.34 84.40 0.71 1.00

S120_s2 32.64 84.80 0.72 0.99

S120_s3 28.13 85.10 0.72 0.88

S120_s5 34.43 86.30 0.73 1.08

S120_s4 27.40 86.50 0.73 0.86

S120_s6 33.71 86.30 0.73 1.08

S140_s1 37.14 100.60 0.73 1.09

S140_s2 38.65 102.20 0.74 1.11

S140_s3 47.47 101.90 0.74 1.16

S140_s4 32.65 99.50 0.72 0.96

S140_s5 38.99 101.00 0.73 1.01

S160_s1 57.85 114.10 0.72 1.19

S160_s2 57.04 115.70 0.73 1.16

S160_s3 56.28 114.40 0.72 1.15

S160_s5 57.96 116.00 0.73 1.22

S160_s6 56.54 115.50 0.73 1.18

S180_s1 85.69 130.80 0.74 1.43

S180_s3 88.00 129.20 0.73 1.44

S180_s4 88.83 131.40 0.74 1.46

S180_s5 88.71 131.50 0.74 1.46

S180_s6 81.20 131.20 0.74 1.38

S200_s1 114.11 150.40 0.76 1.60

S200_s2 97.18 147.80 0.75 1.42

S200_s3 95.81 149.30 0.76 1.40

S200_s4 99.28 148.40 0.75 1.45

Average 54.06±28.70 0.73±0.01 1.16±0.22

72

Table 6.2. Average fracture toughness results of FBD specimens with corresponding diameters

D(mm) Pmin ave (kN) 2ace ave(mm) ace ave/R KICavg+STD(MPa√𝑚)

100 22.75 71.50 0.72 0.93±0.11

120 31.44 85.57 0.72 0.98±0.11

140 38.98 101.04 0.73 1.06±0.09

160 57.13 115.14 0.73 1.18±0.07

180 86.49 130.82 0.74 1.43±0.04

200 101.60 148.98 0.75 1.46±0.09

Average 56.40±31.65 0.73±0.01 1.18±0.23

For a better visualization, KIC values and KIC avg values of FBD specimens having

constant loading angle (2𝛼 = 22°) and various diameters are represented in Figure

6.1. Red dots symbolize average values related to specimen diameter whereas the blue

dots stand for individual results, (Figure 6.1). Curve is fitted to the average results of

each diameter group. Fracture toughness increases with sample size following a fitted

third degree polynomial. The lowest 0.93 MPa√𝑚 for 100 mm size group and the

highest is 1.46 MPa√𝑚 for the 200 mm group. The average fracture toughness

increase is about 57% according to the average of the diameter group.

73

Figure 6.1. KIC values of FBD tested specimens having various diameters

A third-degree polynomial functional fit to the ratios in Figure 6.1 is the best fit and

this fitted function gives an estimated minimum at D=0.107 m as KIC=0.93 MPa√𝑚

and maximum at D=0.205 m as KIC=1.49 MPa√𝑚. According to the extreme points

of the equation, it is predicted that after the diameter increases up to around 205 mm,

the increase in fracture toughness would not continue.

The size effect phenomenon can be clearly observed from Figure 6.1. Mode I fracture

toughness values increase with the specimen diameter. KIC avg for the largest diameter

group (D=200 mm) is about 1.57 times higher than the KIC avg of the smallest diameter

group (D=100 mm). As the specimen gets larger, the crack tip gets further from the

compressively loaded area. In this case, the size of the fracture process zone is

relatively small compared to the specimen dimension, this can explain the reason

behind the higher fracture toughness values at higher diameters. Moreover, another

possible factor that lead to this increase can be explained as confining effect.

74

Shotcrete is heterogeneous material; if a crack is forced to follow a strict path for a

large enough path in a large size disc, crack tip may be forced to break through both

binder and rather strong aggregate grains, resulting in a higher KIC.

During test, cracks initiated at the center of the specimens and propagated toward the

loaded flat ends. A graphical representation of critical dimensionless crack lengths

determined from experimental results for all thirty FBD shotcrete specimens and their

average values for various diameters are shown Figure 6.2. Red dots symbolize

average values calculated related to specimen diameter whereas the blue dots stand

for individual results. Curve fitted to the each diameter group. Dimensionless critical

crack length increases with sample size following a fitted third degree polynomial.

The lowest 0.72 MPa√𝑚 for 100 mm size group and the highest is 0.75 MPa√𝑚 for

the 200 mm group.

Figure 6.2. Dimensionless critical crack length of FBD tested specimens

75

The ace/R ratio increases in specimen diameter. The amount of increase is about 4%.

Normally, ace/R must remain constant at the numerically computed ace/R. This

increase is attributed to the size effect issue in the sense that inertia of unstably moving

crack is greater in a large size sample.

Another observation was that cracks were seen more prominently and clearly as the

specimen diameters grew.

6.2. Effect of Curing Time on the Fracture Toughness

Early-age developed-which designated in this study the period between 1 and 7 days

after casting- 21 shotcrete specimens with constant diameter D=160 mm and constant

loading angle (2a=22°) with 1 day, 2 days, 3 days, 5 days and 7 days cured shotcrete

specimens were subjected to mode I fracture toughness test in order to determine the

effect of curing time on mode I fracture toughness. Again, during all tests, cracks

initiated at the center of the tested specimen and propagated through the flattened ends.

All test results are tabulated in Table 6.3. The averages of each curing time group are

provided in Table 6.4.

76

Table 6.3. All test results for investigation of curing time on the fracture toughness

Name CuringTime(day) Pmin(kN) KIC(MPa√𝑚)

S160-1D-s1 1 33.20 0.69

S160-1D-s2 1 29.42 0.60

S160-1D-s3 1 31.38 0.65

S160-1D-s4 1 33.29 0.69

S160-2D-s1 2 37.28 0.77

S160-2D-s2 2 42.28 0.87

S160-2D-s3 2 36.36 0.75

S160-2D-s4 2 38.85 0.81

S160-3D-s1 3 38.60 0.80

S160-3D-s2 3 39.94 0.82

S160-3D-s3 3 42.28 0.88

S160-3D-s4 3 40.80 0.84

S160-5D-s1 5 56.51 1.15

S160-5D-s2 5 55.83 1.14

S160-5D-s3 5 48.67 1.01

S160-5D-s4 5 51.12 1.06

S160-7D-s1 7 57.85 1.19

S160-7D-s2 7 57.04 1.16

S160-7D-s3 7 56.28 1.15

S160-7D-s4 7 57.96 1.22

S160-7D-s5 7 56.54 1.18

Average 44.83±10.04 0.92±0.21

Table 6.4. Average FBD test results according to the changing curing time

Curing Time

(day)

Pmin ave

(kN)

KICavg

(MPa√m)

1 31.82 0.66

2 38.69 0.80

3 40.41 0.83

5 53.03 1.09

7 57.13 1.18

Average 44.22±10.53 0.91±0.22

77

The average mode I fracture toughness value for 1 day cured shotcrete specimens was

calculated as 0.66 MPa√𝑚 , for 2 days cured shotcrete specimens it was 0.80 MPa√𝑚

, 0.83 MPa√𝑚 for 3 days cured, 1.09 MPa√𝑚 for 5 days cured and for 7 day cured

shotcrete specimens it was calculated as 1.18 MPa√𝑚. Results showed that the

average mode I fracture toughness values of early aged shotcrete specimens were

changing between 0.66-1.18 MPa√𝑚, (Table 6.4).

Based on the test results, determined fracture toughness of two day cured shotcrete

specimens increased approximately by 21% in comparison with the average of 1 day

cured results. The average fracture toughness value for seven day cured shotcrete

specimens increased dramatically from around 21% to 78% in comparison with the

average of 1 day cured test results.

Effect of curing time on mode I fracture toughness can be clearly observed from

Figure 6.5. Curve fitted to the each curing time group. Fracture toughness increases

with increasing curing time following a fitted third degree polynomial.

78

Figure 6.3. Average KIC values changing with the curing time of shotcrete

Fracture Toughness increases with curing time following a fitted third degree

polynomial. The lowest 0.66 MPa√𝑚 for 1 day-cured group and the highest is 1.18

MPa√𝑚 for 7 day-cured group. KIC avg for the seven day-cured group is about 1.78

times higher than the KIC avg of the one day-cured group. The average fracture

toughness increase of about 79% according to the average of the curing time group.

6.3. Tensile Strength - Fracture Toughness Investigation

In below Table 6.5, mode I fracture toughness values for corresponding diameters

from 100 mm to 200 mm and tensile strength results, 𝜎𝑡,𝑊, which was calculated using

Wang’s correction coefficient and relevant FBD test results and tensile strength

results, 𝜎𝑡,𝐾 𝑇 , which was calculated using Keles’ correction coefficient and relevant

test results were tabulated, (Table 6.5).

79

Table 6.5. Tensile strength calculation from Wang’s correction coefficient

Name

tave

(mm)

Pmax ave

(kN)

𝜎𝑡 𝑊

(MPa)

𝜎𝑡 𝐾 𝑇

(MPa)

KICavg+STD

(MPa√𝑚)

S10022 66.62 24.98 2.30 2.33 0.93±0.11

S12022 79.55 37.31 2.40 2.43 0.98±0.11

S14022 83.99 45.77 2.39 2.42 1.06±0.09

S16022 103.86 67.68 2.50 2.53 1.18±0.07

S18022 122.38 102.92 2.87 2.91 1.43±0.04

S20022 133.16 127.14 2.93 2.97 1.46±0.09 ∗ 𝜎𝑡 𝑊 represents calculated tensile strength by using Wang’s approach and 𝜎𝑡 𝐾 𝑇 represents calculated tensile

strength by using Keles and Tutluoglu’s approach.

It is possible to correlate between the mode I fracture toughness values and the tensile

strength. Since in an opening mode, specimen splitting is due to the tensile stress. To

this extent, existence of the same relationship in shotcrete specimen was investigated

in Figure 6.4 and Figure 6.5.

Figure 6.4. The relation between σt W and KIC

80

Both average tensile strength that computed from the Wang’s approach and fracture

toughness increase with sample size following a fitted second-degree polynomial.

Figure 6.5. The relation between σt,K T and KIC

Both average tensile strength that computed from the Keles and Tutluoglu’s approach

and fracture toughness increase with sample size following a fitted second-degree

polynomial.

A second-degree polynomial functional fit to the results in Figure 6.5 is the best fit

and this fitted function gives an estimated maximum at σt =3.26 MPa as KIC=1.52

MPa√𝑚.

These graphs show that calculated tensile strength from the Flattened Brazilian Disc

test is increasing while fracture toughness of the sample is increasing with changing

diameters between 100 mm to 200 mm. The rate of increase of fracture toughness with

tensile strength decreases for larger diameter groups. For shotcrete, size-independent

81

ratio between the fracture toughness and tensile strength is estimated as

KIC/σt=1.52/3.26=0.47 for the first time compared to the related literature.

Advancing this study, dimensionless fracture toughness over tensile strength ratio

changing with specimen size was investigated with tensile strength calculated using

Keles and Tutluoglu’s approach, which is a more recent study, in Figure 6.6.

Figure 6.6. Dimensionless toughness over tensile strength ratio

This polynomial function of degree three becomes zero at D=0.26 m meaning that size

independent fracture toughness and tensile strength is best measured for a diameter

range between 120-180 mm (best D=160 mm) tensile strength; after the tensile

strength increases too rapidly compared to fracture toughness taking curve down to

zero at 0.26 m diameter.

83

CHAPTER 7

7. CONCLUSION AND RECOMMENDATIONS

FBD geometry is used here for measuring the tensile strength and the tensile mode

fracture toughness of the molded shotcrete samples. For the FBD geometry,

compressive load at the flat ends results tension in the center, and crack is forced to

initiate at the center and propagate towards the loaded flattened ends. 3D printing

technology provides great advantages in terms of the accurate sample preparation

geometry for the desired diameter range of testing samples.

Size effect was clearly observed in results of seven day cured FBD testing work.

According to the American Shotcrete Association; concrete, when applied using the

shotcrete process, or cast-in-place, needs to cure for 7 days (American Shotcrete

Association, n.d.). Moreover, according to the American Concrete Institute (ACI)

often specified seven-day curing is recommend as a minimum curing period for Type

I cement in standards ASTM C 150. (Zemajtis, n.d.). Mode I fracture toughness values

at constant loading angle (22°) were increasing with the specimen diameter. The

average mode I fracture toughness, KIC avg for the largest diameter group (D=200 mm)

is about 1.57 times higher than the average mode I fracture toughness, KIC avg of the

smallest diameter group (D=100 mm). As the specimen gets larger, the crack tip gets

further from the compressively loaded area. In this case, the size of the fracture process

zone is relatively small compared to the specimen dimension, this can explain the

reason behind the higher fracture toughness values at higher diameters. Moreover,

another possible factor that lead to this increase can be explained as confining effect.

Shotcrete is a heterogeneous material; if a crack is forced to follow a strict path for a

large enough path in a large size disc, crack tip may be forced to break through both

binder and rather strong aggregate grains, resulting in a higher fracture toughness KIC.

84

According to the extreme points of the equation, it was predicted that after the

diameter increases up to around 205 mm, the increase in fracture toughness would not

continue.

In the size effect investigation, numerically computed and experimentally observed

crack lengths were compared. Shotcrete samples with rather large diameters showed

clearer local minimum load drops in the related load-displacement plots. Compared to

the numerically computed crack length/radius ratio acn/R of constant 0.72, ace/R ratio

increases with specimen diameter. The amount of increase is about 4%. This increase

is attributed to the size effect issue in the sense that inertia of unstably moving crack

is greater in a large size sample.

Considering the fact that shotcrete support unit provides temporary surface control of

underground openings, the effect of curing time on fracture toughness can be a

significant contribution. The early aged mixture design was used for the investigation

of curing time effect on the fracture toughness for specimens having diameter of 160

mm; KIC values increased about 79% with the curing time varying 1 day to 7 days.

In order to study the relation between fracture toughness and tensile strength, the

comparisons were made. After the results of several experimental works, it was

concluded that, up to a certain point tensile strength and the fracture toughness

increases proportionally.

The difference between the tensile strength obtained from the regular Brazilian Disc

test and the Flattened Brazilian Disc test can be explained by two reasons. The first

possible reason is the loading angle of the jaw used in the regular Brazilian Disc Test

is lower than the loading angle of the Flattened Brazilian Disc test. As the loading

angle decreases, fracture toughness is believed to increase, and thus tensile strength

increases too, since as found in this work, fracture toughness and tensile strength

increase proportionally. The second possible reason can be the loading differences.

While regular Brazilian Disc specimen is under an arc type loading because of the

85

steel jaws, the Flattened Brazilian Disc specimen is under the uniform diametrical

compression.

The Size effect phenomenon is effective on tensile strength obtained from the

Flattened Brazilian Disc test. With using two different approaches, Wang’s approach

and Keles & Tutluoglu’s approach, to obtain tensile strength from Flattened Brazilian

Disc tests results, tensile strength is found to increase with increasing diameter from

100 mm to 200 mm. There was a threshold diameter after which strength increased

with increasing disc size. Threshold diameter was around 200 mm.

In this study, for the shotcrete specimens that have 0.5 water/cement ratio, the size

effect on tensile strength was observed between 100 mm diameter and 200 mm. As a

result of fitted third degree polynomial function between the dimensionless fracture

toughness/tensile strength ratio and specimen diameter, the size-independent values

can be calculated in a diameter range between 120-180 mm (the best at 160 mm).

Tensile strength from FBD tests increased with increasing size. Explanation can be in

terms of crack tip stress field and a 3D yield criterion in terms of all principal stresses

(σ1, σ2, σ3). As diameter increases and specimen gets thicker, in-plane minimum

principal stresses and out of plane principal stresses change and perhaps increase in

compression. Use of a single yield criterion based on tensile strength and minimum

principal stress may not be the right approach to characterize the cracking failure for

this geometry. A yield criterion in terms of all principal stresses may be the choice for

describing the tensile cracking and surrounding stress distributions which are to be

inserted to 3-dimensional yield criteria.

For future work, it is suggested to use a stronger mold material to be used in the 3D

printer, since some molds broke before the tests are completed successfully. Another

recommendation is to extend this testing work for specimen sizes larger than the ones

used here. Also curing time work may involve more data points in the early ages of

curing, since this aging process is an important issue in carrying the expected loads in

a temporary support unit.

87

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APPENDICES

A. Static Deformability and Brazilian Disc Test Graphs

Figure 0.1. Static deformability test graph of S_SD_1


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Figure 0.11. Brazilian Disc test graph of S_BD_1


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B. Mode I Fracture Toughness Test Graphs

Figure 0.16. Flattened Brazilian Disc test graph of S100_s1


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Figure 0.46. Flattened Brazilian Disc test graph of S160-1D-s1


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C. Crack Length Measurement of Mode I Fracture Toughness Test Samples

Figure 0.61. FBD test crack measurement of the sample S100_s1


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mode i fracture toughness and tensile strength

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